Related papers: On Statistical Distribution for Adiabatically Isol…
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results precisely…
The gravitational three-body problem is a rich open problem, dating back to Newton. It serves as a prototypical example of a chaotic system and has numerous applications in astrophysics. Generically, the motion is non-integrable and…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor $K(t)$ analytically for a minimal Floquet circuit model that has a $U(1)$ symmetry…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
A shortcut to adiabaticity (STA) is concerned with the fast and robust manipulation of the dynamics of a quantum system that reproduces the effect of an adiabatic process. A recently proposed method enables the generation of shortcuts from…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a…
We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak coupling limit. It is proved that, even when the external field is strong, the…
The stochastic quantization of dissipative systems is discussed. It is shown that in order to stochastically quantize a system with dissipation, one has to restrict the Fourier transform of the space-time variable to the positive half…
A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schroedinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from…
Dynamic state estimation, as opposed to kinematic state estimation, seeks to estimate not only the orientation of a rigid body but also its angular velocity, through Euler's equations of rotational motion. This paper demonstrates that the…
A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform…
Adiabatic quantum computing is a powerful framework for state preparation, while its evolution time often scales quadratically in the inverse Hamiltonian spectral gap, leading to sub-optimal computational complexity. In this work, we…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
We consider quantum statistics of charge transmitted through a mesoscopic device in the adiabatic pumping process. A general formula for the distribution function of the transmitted charge in terms of the time-dependent S-matrix is…
We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of…
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external…
We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival…