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Recently, the study of criticality in quantum systems has attracted significant interest. There is theoretical evidence suggesting the existence of the spin quantum Hall effect (sqHe) in two-dimensional superconducting systems with d_(x^2-y^2 )+i d_xy [1]. In such systems, the quantization of spin conductivity (in even integers of e^2/h) has been demonstrated. Since the sqHe is closely related to the integer quantum Hall effect (iqHe), it is natural to consider whether certain symmetry-breaking mechanisms could induce a crossover between them [2]. In this study [3], we develop a theoretical framework for the crossover from the spin quantum Hall effect to the integer quantum Hall effect. First, we analyze the edge theory of a d_(x^2-y^2 )+i d_xy topological superconductor, as derived in [1]. We demonstrate that the presence of static disorder at the edge leads to the emergence of a topological theta term in the effective diffusive action. This indicates that the quantization of spin conductance remains robust against impurities, and the corresponding action falls within class C of the Altland-Zirnbauer classification [4]. We further show that applying a Zeeman field only at the edge is insufficient to induce a crossover. Next, we examine the bulk (2D) action for class C in the presence of Zeeman symmetry breaking. We show that bulk topological excitations (instantons) change across the crossover. Specifically, we find that instantons with topological charge W=1 are suppressed by the Zeeman field, while instantons with W=2 transform into two Pruisken instantons [5] with W=1. As a result, the quantization of spin conductivity transitions from even integers to all integers. We propose that this spin-to-integer quantum Hall effect crossover could potentially be realized in topological superconductors, such as twisted Bi_2 Sr_2 CaCu_2 O_(8+x). *This work was supported by the Project No. FFWR-2024-0017. [1] T. Senthil, J. B. Marston, and M. P. A. Fisher, Spin quantum Hall effect in unconventional superconductors, Phys. Rev. B 60, 4245 (1999). [2] S. Bhardwaj, I. A. Gruzberg, and V. Kagalovsky, Relevant perturbations at the spin quantum Hall transition, Phys. Rev. B 91, 035435 (2015). [3] M. V. Parfenov, I. S. Burmistrov to be published. [4] A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Classification of topological insulators and superconductors, AIP Conf. Proc. 1134, 10 (2009). [5] A. M. M. Pruisken, Quasiparticles in the theory of the integral quantum Hall effect (I), Nucl. Phys. B 285, 719 (1987).
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We construct N=2 Superconformal Field Theories with modular invariant partition functions and with central charge c=9. Such theories arising after the compactification in superstring theory. Left and right primary fields in these theories are connected according to A-D-E classification. Orbifolds of the product of Minimal Models connected to Calabi-Yau manifolds of Fermat types are considered. We construct the set of mutually local fields, twisted by the elements of the group of symmetry.
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Specific action for isotropic fluctuations of scalar field is derived under the condition of 4D cut-off. It is implemented into the estimates of dark energy scale consistent with current cosmological data.
Institution - Forschungszentrum Jülich, Germany
The Dicke-Ising model, one of the few paradigmatic models of matter-light interaction, exhibits a superradiant quantum phase transition above a critical coupling strength. However, in natural optical systems, its experimental validation is hindered by a \"no-go theorem\". Here, we propose a digital-analog quantum simulator for this model based on an ensemble of interacting qubits coupled to a single-mode photonic resonator. We analyze the system\\'s free energy landscape using field-theoretical methods and develop a digital-analog quantum algorithm, which disentangles qubit and photon degrees of freedom through a parity-measurement protocol. This disentangling enables the emulation of a photonic Schrödinger cat state -- a hallmark of the superradiant ground state in finite-size systems. The cat state can be unambiguously probed through the Wigner tomography of the resonator\\'s field. Our algorithm features a sequence of analog Jaynes-Cummings gates combined with standard digital single-qubit and two-qubit rotations. This quantum circuit is capable of simulating quench dynamics and the quantum phase transition between the normal and superradiant phases. Additionally, we (i) applied a path-integral description to the model via the bosonic angular representation of spin operators and (ii) formulated a quasi-classical description of fluctuations in the large-spin limit. This approach can be useful for further studies of macroscopic quantum tunneling. Finally, we found that the qubit-qubit interaction leads to an emergent Ising transition driven by the Kibble-Zurek mechanism in imaginary time. The qubit subsystem becomes critical for certain quantum trajectories of the photon field, making the fluctuations in the superradiant phase non-trivial, in contrast to the conventional Dicke model. For further details, see our preprint [1]. [1] D. S. Shapiro, Y. Weber, T. Bode, F. K. Wilhelm, D. Bagrets, \"Quantum Simulation of the Dicke-Ising Model via Digital-Analog Algorithms\", arXiv:2412.14285 (2024).
Institution - Indian Institute of Technology Bombay, India
Many-body localization arises from the interplay of interactions and disorder in closed quantum systems, forming an emergent integrable phase, which could have potential applications in modern quantum technologies. In recent years, significant progress has been made in understanding the fragility of the phase, mainly when studied through ensemble-averaged properties within a reasonable parameter regime. A key insight from these studies is the presence of strong sample-to-sample fluctuations in local observables, such as particle density. Here, we take a Fock-space perspective on thermalization dynamics, developing a geometric description of Fock-space connectivity that dominates transient dynamics. Even in the weak disorder regime, certain strongly localized samples can be understood as fragmented Fock-space clusters onto dynamically resonant structures. This highlights the complexity of disorder ensembles, questioning the notion of many-body localized phase in generic model.
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We discuss how the classical phase-locking phemomena arises in quantum mechanical systems. We provide the correspondence between the Poincare rotation number for the 2D dynamical systems on torus of Mobius type and the Schrodinger equation with periodic potential. This correspondence allows us to treat slow-fast dynamics in systems on torus in terms of exact WKB and vice-versa
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We report on the theoretical study of photocurrents arising in direct optical transitions in semiconductor bulk materials and structures taking into account the Coulomb interaction. In macroscopically homogeneous crystals or laterally uniform two-dimensional systems lacking inversion symmetry, an alternating electromagnetic field can induce a steady photocurrent, a phenomenon known as the photogalvanic effect. We develop a theory of the linear interband photogalvanic effect that precisely accounts for the electron-hole Coulomb interaction. For the interband optical transitions, there are two contributions to the linear photocurrent: the shift contribution, caused by the displacement of electron wave packets in the real space during quantum transitions, and the ballistic contribution, originating from asymmetry of the photoelectron distribution in the momentum space. While recent studies of the linear photogalvanic effect have been predominantly focused on the shift contribution [1, 2], it is emphasized in Ref. [3] that the ballistic contribution dominates for interband transitions. We present calculations comparing both contributions within a unified band-structure model for systems of different dimensions. A detailed microscopic theory of shift and ballistic currents is developed, incorporating a self-consistent method to treat Coulomb correlations between the photoexcited electron and hole to all orders of perturbation [4]. The theory is applied to calculate the linear photogalvanic effect in bulk semiconductors with a zinc blende lattice, as well as in two-dimensional materials based on monolayers of transition metal dichalcogenides of the D3h symmetry. It is demonstrated that the Coulomb interaction enhances the shift photocurrent due to an increase in optical absorption due to excitonic effects, although the shift current does exist even neglecting electron-hole scattering. In contrast, the ballistic contribution to the linear photogalvanic effect for direct optical transitions requires an additional scattering to take place, here the Coulomb scattering of a photoexcited electron by a hole. The matrix elements of the velocity operator taken between the Coulomb two-particle functions of the continuous spectrum, including its components off-diagonal in the wave vectors, are calculated in order to obtain the ballistic contribution. Frequency dependencies of the both contributions to the photocurrent are calculated for bulk semiconductors as well as for two-dimensional monolayer structures. It is demonstrated that the ballistic photocurrent can significantly exceed the shift current in both material classes. It is shown that the ratio of the ballistic contribution to the shift contribution scales as l/aB, where l is the charge carriers mean free path and aB is the exciton Bohr radius. As a result, in a wide range of frequencies where the mean free path of photoexcited charge carriers is longer than the Bohr radius, the ballistic contribution dominates. Thus, accounting for Coulomb interaction to the ballistic mechanism yields a substantially larger total photocurrent than shift-only models predict. This work was supported by the Russian Science Foundation (project 22-12-00211). 1. Z. Dai and A. M. Rappe // Phys. Rev. B 104, 235203 (2021). 2. Zhenbang Dai and A. M. Rappe // Chem. Phys. Rev. 4, 011303 (2023). 3. B. I. Sturman // Phys.-Usp. 63, 407 (2020). 4. G. V. Budkin, E. L. Ivchenko // JETP 167, 279 (2025). [arXiv:2409.05571]
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Closed lipid membranes (vesicles), being flexible and incompressible, demonstrate a plethora of non-spherical shapes (especially under simple external influences). Within the framework of the hydrodynamic approach, the bilayer is treated as an infinitely thin liquid film with a surface density of free energy. The starting point for this consideration is Helfrich\\\\\\'s energy [W. Helfrich, Z Naturforsch (1973)] , which depends on vesicle shape. Using hydrodynamic Poisson brackets, we can obtain a non-dissipative contribution to the stress tensor from the membrane. Corresponding surface forces cause flows in the viscous surrounding liquid which make the membrane to move. Although such flows occur at low Reynolds numbers, described by the linear hydrodynamic equation (the Stokes equation), vesicle\\\\\\'s shape changes significantly over time.. This makes the system of dynamic equations highly nonlinear. On the one hand, it determines the complexity of the problem, and on the other hand, leads to the need for numerical modelling of the process. The study investigates the behavior of elongated vesicles under the influence of extending forces, such as uniaxial flow and optical tweezers. There are two critical values of force amplitude: beyond the first, a \\\"dumbbell\\\"-shaped structure forms with a possible infinite elongation, and the second is responsible for the so-called pearling instability, i.e., the formation of beads connected by thin tubes. We also provide a qualitative description of the phenomenon by discussing the variety of stretched shapes and conditions of quasi-stationarity and transition to infinite stretching. In addition, we study the highly nonlinear stage: a slow dynamics remains after the formation of pearls due to the thinness of tubes. Our results qualitatively agree with experimental observations [Kantsler, Segre, and Steinberg (2008)].
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Thin dirty superconducting films containing magnetic impurities exhibit nontrivial behavior when subjected to an applied magnetic field. This behavior manifests itself in the enhancement of superconductivity, which is attributed to the reduction in the exchange scattering rate due to the polarization of the impurity spins in the presence of the magnetic field. This effect was theoretically predicted in Ref. [1] and then observed experimentally in Ref. [2]. In both studies, the authors concentrated on the dependence of the critical temperature on the magnetic field parallel to the film surface, revealing a nonmonotonic behavior characterized by a maximum at finite field values. However, manifestations of this enhancement for other observable physical quantities, as well as the description of the effect in the presence of a magnetic field component perpendicular to the film surface, have not been investigated. To address this gap, we develop a theoretical framework employing Gorkov\\\\\\'s diagrammatic technique for superconductors. Our work expands the theory of Ref. [1] in two directions: (i) we demonstrate that the enhancement is also reflected in an increase in superfluid density and the spectral energy gap; (ii) we reveal a nonmonotonic dependence of the second critical field (perpendicular to the film surface) on the magnetic field component parallel to the surface. [1] M.Yu. Kharitonov and M.V. Feigelman, \\\"Enhancement of superconductivity in disordered films by parallel magnetic field\\\", JETP Lett. 82, 421–425 (2005). [2] Masato Niwata, Ryuichi Masutomi and Tohru Okamoto, \\\"Magnetic-Field-Induced Superconductivity in Ultrathin Pb Films with Magnetic Impurities\\\", Phys. Rev. Lett. 119, 257001 (2017).
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The work is devoted to superconductivity in recently discovered Ising superconductors. This state in them has not yet been fully studied. In particular, the question arises as to which of the valleys in the Brillouin zone play the main role. The central valley Γ is, under certain assumptions, an independent electron subsystem. In the work, we have obtained and analyzed the gauge-invariant effective action of this subsystem. It includes singlet and triplet pairings, and it is necessary to take into account the locality of these interactions, as well as the symmetry of the lattice. In particular, we obtain an expression for the superconducting weight in the subsystem.
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Nonequilibrium properties of superconducting systems have been studied for a long time. One of such properties is enhancement of superconductivity by microwave irradiation, which was explained theoretically by Eliashberg [1,2] by means of Gorkov equations. In 2018 this theory was extended and refined in [3]. However, recently novel mechanism of microwave absorption was suggested [4]. In their paper authors introduce mechanism of absorption, similar to the Debye absorption in molecular gases, which for non-zero current leads to a large contribution to the ac conductivity, which is proportional to the inelastic scattering time $\\\\tau_{in}$. In present work, we consider quasi-one dimensional diffusive superconductor with finite current bias. Within Keldysh non-linear sigma model approach, we computed conductivity, which for small amplitude of microwave irradiation could be treated within linear response formalism. We found that in presence of dc current conductivity acquires a novel contribution, which is responsible for the so called Debye contribution to the conductivity. We calculated this term for a wide range of frequencies of a microwave and established that results are drastically different for small and large values of $\\\\omega$. [1] G. M. Eliashberg. Film superconductivity stimulated by a high-frequency field. Sov. Phys. JETP Lett., 11:186, 1970. [2] B. I. Ivlev and G. M. Eliashberg. Influence of nonequilibrium excitations on the properties of superconducting films in a high-frequency field. Sov. Phys. JETP Lett., 13:464, 1971. [3] K. S. Tikhonov, M. A. Skvortsov, and T. M. Klapwijk. Superconductivity in the presence of microwaves: Full phase diagram. Phys. Rev. B, 97:184516, May 2018. [4] M. Smith, A. V. Andreev, and B. Z. Spivak. Debye mechanism of giant microwave absorption in superconductors. Phys. Rev. B, 101:134508, Apr 2020.
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In superconducting hybrid structures with broken geometric symmetry and symmetry with respect to time reversal, a diode effect occurs, which consists in different critical currents when an supercurrent flows in different directions. The system we are considering is an SN bilayer – two layers of superconductor (S) and normal metal (N) brought into contact. The bilayer is located in an external parallel magnetic field. The properties of the supercurrent flowing along the bilayer perpendicular to the magnetic field are studied. In 2023, an article [1] was published on the study of the diode effect in such a structure. In it, this effect in the MoN/Cu bilayer was studied numerically and experimentally. Numerical calculation and experiment were carried out for a bilayer with a thickness of each layer on the order of several coherence lengths, but thin compared to the London penetration depth, in the dirty limit allowing the application of the Usadel equations. The fact that the thickness of the layers is of the order of the correlation length leads to a nontrivial distribution of the order parameter, and hence the concentration of superconducting electrons along the thickness of the sample. This makes the problem analytically unsolvable in the general case. Our goal is to consider a similar system in extreme cases that allow an analytical solution, in which, nevertheless, many qualitative patterns for critical currents are preserved, as well as to consider the effect of interface resistance on the diode effect. In particular, the dependences of critical currents on the magnetic field are found. A nonmonotonic dependence of the efficiency of the diode effect on the resistance of the interface with the maximum at a certain optimal resistance has also been established. 1. Finite momentum superconductivity in superconducting hybrids: Orbital mechanism / M. Yu. Levichev, I. Yu. Pashenkin, N. S. Gusev, D. Yu. Vodolazov // Phys. Rev. B. — 2023. — Sep. — Vol. 108. — P. 094517. https://link.aps.org/doi/10.1103/ PhysRevB.108.094517.
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This work is devoted to the role of initial correlations in the nonequilibrium evolution of observables in quantum field theory. We show that information about the initial state of the system can be represented as an additional term in the Keldysh action. This term is expressed in terms of the generating functional of the cumulants of the initial Wigner functional. The presence of non-Gaussian correlations manifests itself in the form of additional vertices, each of which is proportional to the corresponding cumulant. Since, generally speaking, there can be infinitely many nonzero non-Gaussian cumulants, it becomes necessary to somehow limit ourselves to a finite number of them. We show that this can be achieved using the formalism of a two-particle irreducible (2PI) effective action. Namely, we demonstrate that only a finite number of cumulants contribute to the equations of motion in the approximation with a finite number of loops in the diagrammatic representation of an effective action. This makes it possible to systematically take into account the cumulants of higher degrees, gradually increasing the number of loops in approximation to effective action. In addition, we show how non-Gaussian initial correlations can generate a non-zero average field in the process of quantum evolution even if it’s value was zero at the initial moment of time.
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A non-perturbative technique within the Schwinger-Keldysh formalism is applied for nonequilibrium quantum systems with non-Gaussian initial conditions. The system has a free part in the form of an oscillator and a quartic interaction term. The correlation function is computed under specific non-Gaussian initial conditions using the Kadanoff-Baym equations in a two-loop approximation. The same results are also derived using perturbation theory, and a comparison is made between the two approaches. Additionally, we present integral-differential equations in phase space for multiple degrees of freedom, applicable to quantum field systems, and calculate the corresponding correlation function.
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We study the hydrodynamic regime of the ratchet effect, i.e., radiation-induced generation of a direct electric current, $J_{\\\\rm rat}$, in an asymmetric dual-grating gate structure without an inversion center. Recently, it was demonstrated that the frequency dependence of $J_{\\\\rm rat}$ is essentially different within the hydrodynamic (HD) and drift-diffusion (DD) regimes of electron transport: $J_{\\\\rm rat}^{\\\\rm HD} \\\\propto 1/\\\\omega^6$ and $J_{\\\\rm rat}^{\\\\rm DD} \\\\propto 1/\\\\omega^2$ for $\\\\omega \\\\to \\\\infty$. Here, we analyze the previously neglected thermoelectric contribution to the ratchet current, $J_{\\\\rm th}$, which arises due to inhomogeneous heating of the electron liquid. We demonstrate that this contribution dominates at sufficiently low electron-phonon scattering rates, yields a high-frequency asymptotic $J_{\\\\rm th} \\\\propto 1/\\\\omega^2$ even in the HD regime, and can change the sign of the response at certain frequency intervals. We analyze the plasmonic resonance in $J_{\\\\rm rat}$, which has the shape of an asymmetric Fano peak, and find that the asymmetry increases with increasing thermoelectric contribution. We also study the effect of finite viscosity of the electron liquid, as well as the manifestation of the plasmonic drag phenomena and inhomogeneous rectification effects in the ratchet current. We demonstrate that viscosity suppresses plasmonic resonance but unexpectedly enhances the Drude peak due to the interference nature of the ratchet effect. This work was supported by the Russian Science Foundation (project 25-12-00212)
Institution - Ljubljana University
We present an analytical calculation of the density of states correlation function in the L´evy-Rosenzweig-Porter random matrix ensemble which off-diagonal elements are strongly non-Gaussian with power-law tails. In order to obtain the results on all the energy scales we use supersymmetry approach. Power-law distribution tails makes the standard Hubbard-Stratonovich transformation inapplicable to such problems. We used, instead, the functional Hubbard-Stratonovich transformation which allowed to solve the problem analytically for large sizes of matrices.
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In this study, we investigate the critical slowing down of dissipative phase transition, which is observed in a parametric oscillator with two-photon drive and both linear and nonlinear dissipation. Using the numerical calculations, complex P-representation and the perturbative, we determine the exponentially small eigenvalue of the Liouville operator that determines small relaxation of the system towards the steady state. Acknowledgment This research was supported by RSF (project No. 21-72-30020).
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In this note we study differential equations for classical blocks with heavy and light operators from different perspectives. We present ODEs for the 4-pt blocks, generalizing the ODE for the 4-pt identity block, found by Fitzpatrick, Kaplan, Walters, and Wang.
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Tunneling is a quantum phenomenon, the essence of which is that the wave function of a system in the course of its dynamics penetrates into the energetically inaccessible region of configuration space. This phenomenon is essentially semiclassical and can be described within the framework of the semiclassical approximation in quantum mechanics by solving the Schrödinger equation by the WKB method. At the same time, there is a wide class of systems for which the description of tunneling within the framework of the Feynman path integral is of interest, in particular, dissipative systems, where the description of the system using the wave function is completely impossible. In such systems, tunneling can be described using the path integral in imaginary time, where the so-called instanton solutions are responsible for tunneling; however, being tied to imaginary time, this formalism is suitable only for studying the characteristics of a system in a state of thermodynamic equilibrium and is not applicable to significantly nonequilibrium phenomena. Hence, it is necessary to develop an approach that takes into account instanton solutions in the framework of the path integral in real time. In this work, a step in this direction is made, consisting in generalizing the Gutzwiller trace formula (which is usually derived in the real-time formalism) for the density of states of a quantum-mechanical particle in a potential with tunneling.
Institution - HSE University
We consider a long and narrow S-TI-S Josephson junction on top of a 3D topological insulator in magnetic field [1,2], surrounded by a layer of insulating magnetic material. Majorana zero modes are predicted to be localized at Josephson vortices in the junction, while the outer edge of the junction supports a 1D Majorana edge mode. Parity of the number of vortices inside of the junction determines the boundary conditions for the edge mode, and in the case of the odd number of vortices, the edge contains a Majorana zero mode. As the global phase difference between the superconductors is varied, the vortices move along the junction. When a vortex approaches the edge of the junction, corresponding Majorana zero mode may hybridize with the Majorana zero mode on the outer edge, acquiring non-zero energy and contributing to the current through the junction. Considering the edge mode scattering problem, we find analytical expression for the energy of Majorana zero modes hybridization. We also discuss the current contribution of the hybridization of higher-energy modes, based on numerical solutions. References [1] Potter A. C., Fu L., Phys. Rev. B 88, 121109 (2013) [2] Yue G. et al.., Phys. Rev. B 109, 094511 (2024)
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Sigma models form a class of field theories that play a crucial role in various branches of modern theoretical and mathematical physics. However, studying these models is challenging due to the highly nonlinear nature of their Lagrangians. There are some specific methods, such as the background field method, that can be used to study these models, but they have some limitations. There is an alternative recently proposed method, called \\\"the first-order GLSM formulation\\\" (or \\\"Gross-Neveu formalism\\\"), for studying sigma models. In this method one cast these models as gauge theories with a finite number of interactions using the idea of symplectic reduction. I will present how this method works for target spaces that are homogeneous Hermitian complex spaces associated with classical Lie groups. Based on joint works with Dmitri Bykov: https://arxiv.org/abs/2306.04555, https://arxiv.org/abs/2407.20423, see also https://arxiv.org/abs/2502.07612
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Several possible mechanisms of current-induced instability have been discovered in 2D electron liquid: amplification of plasma waves due to asymmetric boundary conditions of Dyakonov and Shur [1], change of sign of the radiative decay rate resulting in negative absorption coefficient [2], Cherenkov-type instability arising when drift velocity of current exceeds plasma wave velocity [3] and interplay of different dispersion laws of gated and ungated plasmons [4]. We investigate current-induced plasma wave instability in 2D electron liquid with periodically modulated concentration which creates lateral plasmonic crystal (LPC), recently discussed in [5]. We found that solutions with largest instability increment are excited in particular interval of currents, which is fully determined with electron concentration profile. In this regime, three types of unstable solutions were discovered: the Cherenkov-type instability ω=ω_I+i λ_I with a small increment (ω_I≫λ_I), a new type of unstable solutions with a large increment ω=ω_II+i λ_II (λ_II>ω_II), and a purely imaginary solution ω=i λ_III. Increase of current outside the interval preserves only the first Cherenkov-type instability. This work was supported by the Russian Science Foundation (project 25-12-00212). [1] Dyakonov, Shur // PRL 71, 2465 (1993). [2] Mikhailov // PRB 58, 1517 (1998). [3] Kachorovskii, Shur // APL 100, 232108 (2012). [4] Petrov, Svintsov, Ryzhii, Shur // PRB 95, 045405 (2017). [5] Gorbenko, Kachorovskii // PRB 110, 155406 (2024).
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Consider an $n\\\\\\\\times k$ matrix of i.i.d. Bernoulli random numbers with some value of $p$. Dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe $\\\\\\\\GL_{n}\\\\\\\\times \\\\\\\\GL_{k}$-duality. Thus the probability measure on zero-ones matrix leads to the probability measure on Young diagrams propor-tional to the ratio of the dimension of $\\\\\\\\GL_{n}\\\\\\\\times \\\\\\\\GL_{k}$-representation and the dimension of the exterior algebra $\\\\\\\\bigwedge\\\\\\\\left(\\\\\\\\CC^{n}\\\\\\\\otimes\\\\\\\\CC^{k}\\\\\\\\right)$. Similarly, by applying Proctor\\\\\\\\\\\\\\'s algorithm based on Berele\\\\\\\\\\\\\\'s modification of the Schensted insertion, we get skew Howe duality for the pairs of groups $\\\\\\\\Sp_{2n}\\\\\\\\times \\\\\\\\Sp_{2k}$. In the limit when $n,k\\\\\\\\to\\\\\\\\infty$ $\\\\\\\\GL$-case is relatively easily studied by use of free-fermionic representation for the correlation kernel. But for the symplectic groups there is no convenient free-fermionic representation. We use Christoffel transformation to obtain the semiclassical orthogonal polynomials for $\\\\\\\\Sp_{2n}\\\\\\\\times \\\\\\\\Sp_{2k}$ from Krawtchouk polynomials that describe $\\\\\\\\GL_{2n}\\\\\\\\times\\\\\\\\GL_{2k}$ case. We derive an integral representation for semiclassical polynomials. The study of the asymptotic of this integral representation gives us the description of the limit shapes and fluctuations of the random Young diagrams for symplectic groups. The studied problem is closely connected with describing the moduli space of isomonodromic deformations of rational d-connections as a Sakai surface for discrete Painlevé equations.
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Nonequilibrium quantum field theory is an important area of modern physics, where many arising problems require consideration of the unitary evolution of observables from some initial state of the system, which is not, generally speaking, an proper state for the corresponding Hamiltonian. In this case, the system, being in a nonequilibrium initial state, evolves over time to some equilibrium. One way to specify an initial nonequilibrium state is to instantly change the parameters of the system at the initial moment of time. In such case of creating nonequilibrium, we speak of a quantum quench. In this paper, we study the evolution of a quantum scalar field (and others) as a result of a local quantum quench, i.e. as a result of a rapid perturbation in the vicinity of a certain point. The problem is studied in the formalism of the Keldysh technique, which is convenient for considering nonequilibrium quantum systems. We study the semiclassical approximation, which is exact for non-interacting systems. To calculate the values of observables in the semiclassical approximation, a numerical code is used that calculates a functional integral using the Monte Carlo method. In the general case, to find a semiclassical solution, it is necessary: Find classical trajectories as functions of the initial conditions Calculate the desired observables on the obtained trajectories Average the obtained expressions over the initial conditions with a weight specified by the Wigner functional corresponding to the problem being solved By considering various types of quantum local quenches for various initial states, we study the properties of the corresponding system when a disturbance propagates in it.
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We study the stability of classical solutions in Horndeski theory. In this work, we address a general dynamical spherically symmetric background. We derive the set of stability conditions in the cubic subclass of Horndeski theory and formulate the no-go theorem for this subclass. For full Horneski theory and beyond Horndeski theory we formulate a set of linear stability conditions for high energy odd parity perturbation modes above an arbitrary solution. In this general setting we derive speeds of propagation in both radial and angular directions for gravity waves and compare them with the speed of light in the case of minimally coupled photon. In particular, we find that the class of beyond Horndeski theories, which satisfy the equality of gravity waves’ speed to the speed of light over a cosmological background, feature gravity waves propagating at luminal speeds above a time-dependent inhomogeneous background as well. We revisit the models recently derived from a Kaluza-Klein compactification of higher dimensional Horndeski theory, where the resulting electromagnetic sector features non-trivial couplings to Horndeski scalar. In particular, this class of theories admits the electromagnetic waves propagating at non-unit speed, which in turn allows to relax the constraints on Horndeski theories following from multi-messenger speed test. In this work we prove that both gravitational wave and its electromagnetic counterpart propagate at the same, although non-unit, speed above an arbitrarily time-dependent, spherically symmetric background within the theories in question. Hence, we support the statement that several subclasses of Horndeski theories are not necessarily ruled out after the GW170817 event provided the photon-Galileon couplings are allowed. We also formulate the set stability conditions based on odd parity perturbations for an arbitraty solution within the discussed theoretical setting.
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Non-petrubative partition functions of quantum theories constitute a class of τ −functions, which satisfy Hirota’s bilinear identities. To make this statement general, there must be a proper definition of τ −function, that gives rise to a set of bilinear identities. In the classical definition of τ −function for integrable Toda or KP hierarchies, there is a restriction on matrix elements to be based on group elements with the following comultiplication ∆(g) = g ⊗ g. This restriction cannot be straightforwardly transferred to the q-deformed case because there are no group elements in q-deformed UEA, except for its Cartan subalgebra. The new approach to the τ −function is to remove the restriction on the group elements and replace it with X, where ∆(X) = \\\\sum(X′α ⊗ X′′α) . The main result of this work is the derivation of the set of bilinear identities and τ −functions for Uq (sl3) in both fundamental representations for non-group elements.
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t is known, that Macdonald polynomials are eigen functions of the relativistic generalization of the Calogero-Sutherland hamiltonian. This hamiltonian can be viewed as a part of an integrable system, that corresponds to a certain ”ray” in the representation of DIM-algebra, where central charges have values (0, 0). These ray is nothing but a representation of a commutative subalgebra in DIM, and thus it is possible to construct a complete set of their eigen functions, Baker-Akhiezer functions. It is also possible to generalize this by considering some other commutative subalgebras and their Baker-Akhiezer functions. But an expression for these generalized Baker-Akhiezer functions is only known up to coefficients. In this paper a set of approaches to obtain an expression for these coefficients will be considered. The main idea is to use properties of double affine Hecke algebra (DAHA), which appears to be closely related to this representation. References: [1] A. Mironov, A. Morozov, A. Popolitov. On Chalykh’s approach to eigen- functions of DIM-induced integrable Hamiltonians. [2] A. Mironov, A. Morozov, A. Popolitov. Commutative families in DIM alge- bra, integrable many-body systems and q,t matrix models [3] I. Cherednik. Double Affine Hecke Algebras. [4] O. Chalykh. Macdonald polynomials and algebraic integrability.
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We have studied the transport properties of a system including a superconducting wire interacting with an arbitrary number of normal Fermi reservoirs (leads) and baths. The presence of the latter results in the appearance of a dissipative component of the dynamics in the equation for the density matrix. Within the quantum-field approach with a quadratic Liouvillian, we have obtained expressions for the particle and energy currents in the arbitrary lead, as well as the loss current caused by dissipative processes. Equations for nonequilibrium occupation numbers are obtained taking into account the particle gain/loss processes due to the baths. Based on the conductance analysis, the possibility to probe the degeneracy of a nonequilibrium steady state induced by the nontrivial topology of a closed system is investigated.
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The search for conditions supporting degenerate steady states in nonequilibrium topo- logical superconductors is important for advancing dissipative quantum engineering, a field that has attracted significant research attention over the last decades [1, 2, 3]. In this study, we address this problem by investigating topological superconductors hosting unpaired Majorana modes under the influence of environmental dissipative fields. Within the Gorini-Kossakowski-Sudarshan- Lindblad (GKSL) framework and the third quantiza- tion formalism, we establish a correspondence between equilibrium Majorana zero modes and nonequilibrium master zero modes. We further derive a simple algebraic relation between the numbers of these excitations, expressed in terms of hybridization between the single-particle wavefunctions and linear dissipative fields. Based on these findings, we propose a practical recipes to stabilize degenerate steady states in topological supercon- ductors through controlled dissipation engineering. To demonstrate their applicability, we implement our general framework in the class-BDI Kitaev chain with long-range hopping and pairing terms — a system known to host a robust edge-localized Majorana modes [4]. Our analysis reveals that while master zero modes formally generalize Majorana modes to nonequilibrium settings, key entanglement features of the later can be suppressed under dissipative effects. The work was funded by Russian Ministry of Science and Higher Education (Project No. FFWR-2024-0017). The authors acknowledge personal support from the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” References: [1] S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. Buchler, and P. Zoller, Nat. Phys. 4, 878–883 (2008). [2] F. Thompson and A. Kamenev, Ann. Phys. (N.Y.) 455, 169385 (2023). [3] L. M. Sieberer, M. Buchhold, J. Marino, and S. Diehl, arXiv:2312.03073 (2023). [4] L. Fidkowski, A. Kitaev, Phys. Rev. B 83, 075103 (2023)
Institution - Alikhanyan National Science Laboratory
We demonstrate how disorder and strong interactions in flat‐band systems provide a unified route to Sachdev-Ye-Kitaev (SYK) physics and non-Fermi-liquid behavior across two complementary platforms. In an optical Kagome lattice, randomly positioned immobile impurities localize a flat band into a tunable, all-to-all complex Fermion network, allowing direct equilibrium and non-equilibrium measurements. In magic-angle twisted bilayer graphene on disordered substrates, inhomogeneities fragment the nearly flat moiré bands into mesoscopic \"SYK bundles,\" whose incoherent interbundle tunneling yields linear-in-T transport. Together, these realizations establish disordered interacting flat bands as a versatile experimental arena for exploring quantum chaos, strange‐metal transport, and emergent holographic dualities.
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Correlated quantum many-body states can be created and controlled by the dissipative protocols. Among these, particle number-conserving protocols are particularly appealing due to their ability to stabilize topologically nontrivial phases. Is there any fundamental limitation to their performance? We address this question by examining a general class of models involving a two-band fermion system subjected to dissipation designed to transfer fermions from the upper band to the lower band. By construction, these models have a guaranteed steady state — a dark state — with a completely filled lower band and an empty upper band. In the limit of weak dissipation, we derive equations governing the long-wavelength and long-time dynamics of the fermion densities and analyze them numerically. These equations belong to the Fisher-Kolmogorov-Petrovsky-Piskunov reaction-diffusion universality class. Our analysis reveals that the engineered dark state is generically unstable, giving way to a new steady state with a finite density of particles in the upper band. We also estimate the minimum system sizes required to observe this instability in finite systems. Our results suggest that number-conserving dissipative protocols may not be a reliable universal tool for stabilizing dark states.
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In this paper, we consider a quantum integrable system related to the affine Yangian Y(gl(2)), in the Wakimoto realization of the underlying space. Starting from the Lax operator, we compute R-matrix at the lowest levels and reveal a nice sl(2) structure on the vacuum subspace. Furthermore, we establish a correspondence between a zero-twist frame and stripped two-sheaved partitions. Finally, we construct Bethe vectors and derive Bethe Ansatz equations.