相关论文: Quantum Hamiltonians and Stochastic Jumps

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…

Quadratic Hamiltonians are important in quantum field theory and quantum statistical mechanics. Their general studies, which go back to the sixties, are relatively incomplete for the fermionic case studied here. Following Berezin, they are…

Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics.…

The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a…

From the time dependence of states of one of them, the dynamics of two interacting qubits is determined to be one of two possibilities that differ only by a change of signs of parameters in the Hamiltonian. The only exception is a simple…

We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…

Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$…

The dynamics of the eigenvalues (semimartingales) of a L\'{e}vy process $X$ with values in Hermitian matrices is described in terms of It\^{o} stochastic differential equations with jumps. This generalizes the well known Dyson-Brownian…

We in this paper study the quantization of a particle in an inverted potential well. The Hamiltonian is Hermitian, while the potential is unbounded below. Classically the particle moves away acceleratingly from the center of potential top.…

I argue that Bohmian mechanics (or any similar pilot-wave theory) cannot reasonably be claimed to be a deterministic theory. If one assumes the "quantum equilibrium distribution" provided by the wave function of the universe, Bohmian…

An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the…

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in…

The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…

When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…

In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form…

In the previous paper, it has been proved that elastic scattering processes of two quantum particles are always accompanied with nonlocal processes. Furthermore, it is found that setting an additional Hamiltonian after the originally…

Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation. Although the…

We solve two long standing problems for stochastic descriptions of open quantum system dynamics. First, we find the classical stochastic processes corresponding to non-Markovian quantum state diffusion and non-Markovian quantum jumps in…

We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is…