Related papers: Area Potentials and Deformation Quantization
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
Quantifiers of stationarity, classicality, purity and vorticity are derived from phase-space differential geometrical structures within the Weyl-Wigner framework, after which they are related to the hyperbolic stability of classical and…
The quantum phase-space dynamics driven by hyperbolic P\"oschl-Teller (PT) potentials is investigated in the context of the Weyl-Wigner quantum mechanics. The obtained Wigner functions for quantum superpositions of ground and first-excited…
It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…
In this thesis concrete quantum systems are investigated in the framework of the environment induced decoherence. The focus is on the dynamics of highly nonclassical quantum states, the Wigner function of which are negative over some…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative system. Here, as an application of this formalism, we consider a dissipative system of charged…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
A new scheme for the computation of dispersive interactions from first principles is presented. This cost-effective approach relies on a Wannier function representation compatible with density function theory descriptions. This is an…
We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
We explore the role of majorization theory in quantum phase space. To this purpose, we restrict ourselves to quantum states with positive Wigner functions and show that the continuous version of majorization theory provides an elegant and…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in…
I briefly review the role of the Wigner function in the study of the quantum-to-classical transition through interaction with the environment (decoherence).