相关论文: Sewing sound quantum flesh onto classical bones

We obtain an initial value representation for the quantum Loschmidt echo from the semiclassical theory of Wigner function evolution, together with classical first-order perturbation theory. In the limit of small actions, the amplitude of…

Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…

Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of…

A closed (in terms of classical data) expression for a transition amplitude between two generalized coherent states associated with a semisimple Lee algebra underlying the system is derived for large values of the representation highest…

We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…

The phase space Koopman-van Hove (KvH) equation can be derived from the asymptotic semiclassical analysis of partial differential equations. Semiclassical theory yields the Hamilton-Jacobi equation for the complex phase factor and the…

Starting from the Keldysh theory, for a general low energy $N$-band Hamiltonian in the clean limit, we perform a manifestly $\smash{U(1) \times SU(N)}$ gauge invariant semiclassical expansion. A generalized Berry curvature tensor is shown…

We prove that if $H$ denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph $(X,b,m)$, and if $v:X\to \mathbb{R}$ is such that $H+v/\hbar$ is well-defined as a form sum for all…

We present a mixed quantum-classical approach to strong-field ionization - a semiclassical two-step model with quantum input. In this model the initial conditions for classical trajectories that simulate electron wave packet after…

The scattering theory of Lax and Phillips, originally developed to describe resonances associated with classical wave equations, has been recently extended to apply as well to the case of the Schroedinger equation in the case that the wave…

We consider an inverted harmonic oscillator in the space $L^{2} (\mathbb{S})$ of square-integrable functions on the circle $\mathbb{S}$ and compute its density of states employing the stationary phase approximation. Our computation is based…

Assume that $f$ is a continuous transformation $f:S^1 \to S^1$. We consider here the cases where $f$ is either the transformation $f(z)=z^2$ or $f$ is a smooth diffeomorphism of the circle $S^1$. Consider a fixed continuous potential…

A classical representation for quantum eigenstates of a particle bound in $\lambda z^{2m}$ $(\lambda >0, m=1,2,...)$ potentials is developed. It is represented by ensembles of classical trajectories with energy distributions that can take…

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…

The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…

The notion of Loschmidt echo (also called "quantum fidelity") has been introduced in order to study the (in)-stability of the quantum dynamics under perturbations of the Hamiltonian. It has been extensively studied in the past few years in…

This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to…

We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral…

The target space $M_{p,q}$ of $(p,q)$ minimal strings is embedded into the phase space of an associated integrable classical mechanical model. This map is derived from the matrix model representation of minimal strings. Quantum effects on…

We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…