Related papers: Sharp values for all dynamical variables via Anti-…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
This paper establishes a natural quantum counterpart of weak equilibration for statistical ensembles in integrable systems. For quantum systems with pure point spectrum, single-time expectation values under unitary evolution are typically…
I present a relativistic covariant version of the Bohmian interpretation of quantum mechanics and discuss the corresponding measurable predictions. The covariance is incoded in the fact that the nonlocal quantum potential transforms as a…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
The Husimi distribution is proposed for a phase space analysis of quantum phase transitions in the Dicke model of spin-boson interactions. We show that the inverse participation ratio and Wehrl entropy of the Husimi distribution give sharp…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states…
In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schr\"odinger quantum mechanics by an…
The quantum states representing classical phase space are given, and these are used to formulate quantum statistical mechanics as a formally exact double perturbation expansion about classical statistical mechanics. One series of quantum…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space.…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
We introduce a variational method for simulating the dynamics of interacting open quantum spin systems. The method is based on the spin phase-space representation and variationally targets the Husimi-$Q$ function with an ansatz based on a…
Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism,…