Related papers: New Phase Space Formulations and Quantum Dynamics …
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
This paper is a sequence of the work presented in [1], where, the principles of the general relativity have been used to formulate quantum wave equations taking into account the effect of the electromagnetic and strong interactions in the…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
The constraint coordinate-momentum \textit{phase space} (CPS) has recently been developed to study nonadiabatic dynamics in gas-phase and condensed-phase molecular systems. Although the CPS formulation is exact for describing the discrete…
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys.…
The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
The problem of finding a vacuum definition for a single quantum field in curved space-times is discussed under a new geometrical perspective. The phase space dynamics of the quantum field modes are mapped to curves in a 2-dimensional…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations.…
We present BRST gauge fixing approach to quantum mechanics in phase space. The theory is obtained by $\hbar$-deformation of the cohomological classical mechanics described by d=1, N=2 model. We use the extended phase space supplied by the…