Related papers: Quasi-hermitian Quantum Mechanics in Phase Space
We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the…
A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an…
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…
Three different methods viz. i) a perturbative analysis of the Schr\"odinger equation ii) abstract differential geometric method and iii) a semiclassical reduction of the Wheeler-Dewitt equation, relating Pancharatnam phase to vacuum…
The phase space representation for a q-deformed model of the quantum harmonic oscillator is constructed. We have found explicit expressions for both the Wigner and Husimi distribution functions for the stationary states of the…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum.…
We discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…
A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still missing. In order to fill this gap we extend the so-called fidelity approach to quantum…
The practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians is discussed as requiring an explicit reconstruction of the {\em ad hoc} Hilbert-space metrics which would render the time-evolution…
The Hamiltonian flow of a classical, time-independent, conservative system is incompressible, it is Liouvillian. The analog of Hamilton's equations of motion for a quantum-mechanical system is the quantum-Liouville equation. It is shown…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous…
We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-$\tfrac{1}{2}$ systems. We develop a…
Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide approximation formulas for the expansion of a general Gaussian symbol in terms of elementary…
We study quantum mechanics on a curved wire by approximating the physics around the curved region by three parameters coming from the boundary conditions given by the two interval Sturm-Liouville theory. Since the geometric potential on a…
The deformation star product of smooth functions on the momentum phase space of covariant (polysymplectic) Hamiltonian field theory is introduced.
In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics, we develop a {\it quantum-deformed} exterior calculus on the phase-space of an arbitrary hamiltonian system. Introducing additional bosonic and fermionic…