V. E. Kravtsov
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View article: Renormalization group for Anderson localization on high-dimensional lattices
Renormalization group for Anderson localization on high-dimensional lattices Open
We discuss the dependence of the critical properties of the Anderson model on the dimension d in the language of β -function and renormalization group recently introduced in Vanoni et al. [C. Vanoni et al. , Proc. Natl. Acad. Sci. U.S.A. 1…
View article: Universal Relation between Spectral and Wavefunction Properties at Criticality
Universal Relation between Spectral and Wavefunction Properties at Criticality Open
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and …
View article: Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach Open
By using the Efetov’s super-symmetric formalism we computed analytically the mean spectral density \rho(E) for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-…
View article: Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach Open
By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $ρ(E)$ for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tai…
View article: Renormalization group analysis of the Anderson model on random regular graphs
Renormalization group analysis of the Anderson model on random regular graphs Open
We present a renormalization group (RG) analysis of the problem of Anderson localization on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The RG …
View article: Renormalization group for Anderson localization on high-dimensional lattices
Renormalization group for Anderson localization on high-dimensional lattices Open
We discuss the dependence of the critical properties of the Anderson model on the dimension $d$ in the language of $β$-function and renormalization group recently introduced in Ref.[arXiv:2306.14965] in the context of Anderson transition o…
View article: Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
Renormalization Group Analysis of the Anderson Model on Random Regular Graphs Open
We present a renormalization group analysis of the problem of Anderson localization on a Random Regular Graph (RRG) which generalizes the renormalization group of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional g…
View article: Report on scipost_202210_00061v1
Report on scipost_202210_00061v1 Open
We study coherent forward scattering (CFS) in critical disordered systems, whose eigenstates are multifractals.We give general and simple arguments that make it possible to fully characterize the dynamics of the shape and height of the CFS…
View article: Sensitivity of (multi)fractal eigenstates to a perturbation of the Hamiltonian
Sensitivity of (multi)fractal eigenstates to a perturbation of the Hamiltonian Open
We study the response of an isolated quantum system governed by the Hamiltonian drawn from the Gaussian Rosenzweig-Porter random matrix ensemble to a perturbation controlled by a small parameter. We focus on the density of states, local de…
View article: Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation
Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation Open
The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of…
View article: Report on scipost_202111_00039v1
Report on scipost_202111_00039v1 Open
The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across the many-body localization transition in static systems.We propose a unitary (circula…
View article: Dynamical phases in a ``multifractal'' Rosenzweig-Porter model
Dynamical phases in a ``multifractal'' Rosenzweig-Porter model Open
We consider the static and the dynamical phases in a Rosenzweig-Porter (RP) random matrix ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival proba…
View article: Method for Phase Noise Impact Compensation in 60 GHz OFDM Receivers
Method for Phase Noise Impact Compensation in 60 GHz OFDM Receivers Open
This paper presents a method for phase noise impact compensation in 60 GHz OFDM receivers and provides the results of performance evaluation using OFDM PHY parameters defined in the IEEE 802.11ay standard. It is shown that the phase noise …
View article: Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble
Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble Open
Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase and ergodic transition have a status of a mathematical theorem. Yet, this phase in GRP model is oversimplified: the spectrum of …
View article: Correlation-induced localization
Correlation-induced localization Open
A new paradigm of Anderson localization caused by correlations in the\nlong-range hopping along with uncorrelated on-site disorder is considered which\nrequires a more precise formulation of the basic localization-delocalization\nprinciple…
View article: Electron-phonon cooling power in Anderson insulators
Electron-phonon cooling power in Anderson insulators Open
First microscopic theory for electron-phonon energy exchange in Anderson insulators is developed. The major contribution to the cooling power as a function of electron temperature is shown to be directly related to the correlation function…
View article: Duality in Power-Law Localization in Disordered One-Dimensional Systems
Duality in Power-Law Localization in Disordered One-Dimensional Systems Open
The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, 1/r^{a}. For randomly spaced particles, these models present an effective peculiar disorder that…
View article: Multifractal metal in a disordered Josephson junctions array
Multifractal metal in a disordered Josephson junctions array Open
We report the results of the numerical study of the non-dissipative quantum\nJosephson junction chain with the focus on the statistics of many-body wave\nfunctions and local energy spectra. The disorder in this chain is due to the\nrandom …
View article: Algebraic localization in disordered one-dimensional systems with long-range hopping
Algebraic localization in disordered one-dimensional systems with long-range hopping Open
The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that…
View article: Conduction in quasiperiodic and quasirandom lattices: Fibonacci, Riemann, and Anderson models
Conduction in quasiperiodic and quasirandom lattices: Fibonacci, Riemann, and Anderson models Open
We study the ground state conduction properties of noninteracting electrons in aperiodic but nonrandom one-dimensional models with chiral symmetry and make comparisons against Anderson models with nondeterministic disorder. The first model…
View article: Nonergodic Phases in Strongly Disordered Random Regular Graphs
Nonergodic Phases in Strongly Disordered Random Regular Graphs Open
We combine numerical diagonalization with semianalytical calculations to prove the existence of the intermediate nonergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized popul…
View article: Multifractal states in self-consistent theory of localization: analytical solution
Multifractal states in self-consistent theory of localization: analytical solution Open
We consider disordered tight-binding models which Green's functions obey the self-consistent cavity equations . Based on these equations and the replica representation, we derive an analytical expression for the fractal dimension D_{1} tha…
View article: Non-ergodic phases in strongly disordered random regular graphs
Non-ergodic phases in strongly disordered random regular graphs Open
We combine numerical diagonalization with a semi-analytical calculations to prove the existence of the intermediate non-ergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized p…
View article: Multifractality of random eigenfunctions and generalization of Jarzynski equality
Multifractality of random eigenfunctions and generalization of Jarzynski equality Open
Systems driven out of equilibrium experience large fluctuations of the dissipated work. The same is true for wavefunction amplitudes in disordered systems close to the Anderson localization transition. In both cases, the probability distri…