scholarly journals Phase-space formulation of filtering: insight into the wave-particle duality

2005 ◽  
Vol 22 (3) ◽  
pp. 633
Author(s):  
Daniela Dragoman
Keyword(s):  
Phase Space ◽  
Wave Particle Duality ◽  
Space Formulation ◽  
Insight Into

scholarly journals Reality of the Wigner Functions and Quantization

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Sadollah Nasiri ◽  
Samira Bahrami
Keyword(s):  
Phase Space ◽  
Quantum Statistical Mechanics ◽  
Direct Consequence ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Reality Condition ◽  
Energy Quantization ◽  
Extended Action ◽  
Space Formulation ◽  
Quantum Statistical

Here we use the extended phase space formulation of quantum statistical mechanics proposed in an earlier work to define an extended lagrangian for Wigner's functions (WFs). The extended action defined by this lagrangian is a function of ordinary phase space variables. The reality condition of WFs is employed to quantize the extended action. The energy quantization is obtained as a direct consequence of the quantized action. The technique is applied to find the energy states of harmonic oscillator, particle in the box, and hydrogen atom as the illustrative examples.

scholarly journals Phase space formulation of the Abelian and non-Abelian quantum geometric tensor

2020 ◽  
Vol 53 (50) ◽  
pp. 505305
Author(s):  
Diego Gonzalez ◽  
Daniel Gutiérrez-Ruiz ◽  
J David Vergara
Keyword(s):  
Phase Space ◽  
Space Formulation

scholarly journals xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 290 ◽  
Author(s):  
Ivan Agullo ◽  
Javier Olmedo ◽  
Vijayakumar Sreenath
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Computational Algorithm ◽  
Tensor Algebra ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Bianchi I ◽  
Space Formulation

This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann–Lemaître–Robertson–Walker spacetimes is straightforward.

scholarly journals Dynamics of The Tranquil Cosmic Web

2014 ◽  
Vol 11 (S308) ◽  
pp. 77-86
Author(s):  
Adi Nusser
Keyword(s):  
Phase Space ◽  
Structure Formation ◽  
Observational Data ◽  
Space Distribution ◽  
Phase Space Distribution ◽  
Redshift Surveys ◽  
Data Analyses ◽  
Galaxy Redshift ◽  
Insight Into

AbstractThe phase space distribution of matter out to ∼ 100 \rm Mpc is probed by two types of observational data: galaxy redshift surveys and peculiar motions of galaxies. Important information on the process of structure formation and deviations from standard gravity have been extracted from the accumulating data. The remarkably simple Zel'dovich approximation is the basis for much of our insight into the dynamics of structure formation and the development of data analyses methods. Progress in the methodology and some recent results is reviewed.

scholarly journals Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay

2018 ◽  
Vol 32 (25) ◽  
pp. 1850276 ◽  
Author(s):  
Ludmila Praxmeyer ◽  
Konstantin G. Zloshchastiev
Keyword(s):  
Phase Space ◽  
Density Operator ◽  
Quantum Systems ◽  
Matrix Approach ◽  
Weyl Transform ◽  
Energy Eigenvalues ◽  
Decay Constants ◽  
Dissipative Effects ◽  
Mean Lifetime ◽  
Space Formulation

The Wigner–Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean lifetime and decay constants of quantum systems do not necessarily take arbitrary values, but could become functions of energy eigenvalues and have a discrete spectrum. It is demonstrated also that a constraint upon mean lifetime and energy appears, which is used to derive the resonance conditions at which long-lived states occur. The latter indicate that quantum dissipative effects do not always lead to decay but, under certain conditions, can support stability of a system.

Phase-Space Approach to Berry Phases

2006 ◽  
Vol 13 (01) ◽  
pp. 67-74 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Wigner Function ◽  
Berry Phase ◽  
Space Formulation ◽  
Berry Phases ◽  
Classical Phase Space ◽  
New Formula ◽  
Space Approach

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

scholarly journals LIGHT-CONE GAUGE HAMILTONIAN FOR AdS4 × ℂℙ3 SUPERSTRING

2010 ◽  
Vol 25 (15) ◽  
pp. 1251-1265 ◽  
Author(s):  
D. V. UVAROV
Keyword(s):  
Phase Space ◽  
Light Cone ◽  
Flat Space ◽  
Quadratic Approximation ◽  
Light Cone Gauge ◽  
Space Formulation ◽  
Physical Variables

We develop the phase-space formulation for the Type IIA superstring on the AdS4 × ℂℙ3 background in the κ-symmetry light-cone gauge for which the light-like directions are taken from the D = 3 Minkowski boundary of AdS4. After fixing bosonic light-cone gauge, the superstring Hamiltonian is expressed as a function of the transverse physical variables and in the quadratic approximation corresponds to the light-cone gauge-fixed IIA superstring in flat space.

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