相关论文: Quantum Hamiltonians and Stochastic Jumps

The violation of Bell type inequalities in quantum systems manifests that quantum states cannot be described by classical probability distributions. Yet, Bohmian mechanics is a realistic, non-local theory of classical particle trajectories…

In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct…

Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…

The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…

Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum…

We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for…

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…

Identifying unknown Hamiltonians from their quantum dynamics is a pivotal challenge in quantum technologies. In this paper, we introduce Hamiltonian recognition, a framework that bridges quantum hypothesis testing and quantum metrology,…

A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic Quantum Field Theories to generate dynamics for the…

In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…

A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…

We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…

Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.

Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…

We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…

In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the…

Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…

We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…

In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence, that is believed to restore…