Related papers: Quantum decay rates in chaotic scattering
We prove that the size of the spectral gaps of weakly coupled quasi-periodic Schr\"odinger operators with Liouville frequencies decays exponentially. As an application, we obtain the homogeneity of the spectrum.
We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
The quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a…
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to…
Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by…
We study the quantum probability to survive in an open chaotic system in the framework of the van Vleck-Gutzwiller propagator and present the first such calculation that accounts for quantum interference effects. Specifically we calculate…
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…
Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm…
The decay of quasi-stable quantum system involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although…
We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normal hyperbolic trapping means that the trapped set is smooth and symplectic and that the flow is hyperbolic…
In this paper we analyze the classical limit of the Nelson model with cut off, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum observables to the solutions of classical…
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…
For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents…
In this paper we develop a systematic approach to determine the classical limit of periodic quantum systems and applied it successfully to the problem of the quantum bouncer. It is well known that, for periodic systems, the classical…
Chaotic eigenstates of quantum systems are known to localize on either side of a classical partial transport barrier if the flux connecting the two sides is quantum mechanically not resolved due to Heisenberg's uncertainty. Surprisingly, in…
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schr\"odinger cat state,…
[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…
We analytically model a one-dimensional lattice with periodic impurities representing a photonic crystal from first principles. We then investigate bound states in the continuum by computing the transmission and reflection coefficients. It…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…