Coherent states on lie groups and evolution operator of a system of interacting bosons and fermions

1977 ◽  
Vol 30 (2) ◽  
pp. 139-145 ◽  
Author(s):  
L. F. Novikov
Keyword(s):  
Lie Groups ◽  
Coherent States ◽  
Evolution Operator

scholarly journals Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau
Keyword(s):  
Fourier Analysis ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
Coherent States ◽  
Geometric Theory ◽  
Plancherel Formula ◽  
Group Representations ◽  
Modern Development ◽  
Xxist Century

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

Evolution operator and stable coherent states

1977 ◽  
Vol 60 (5) ◽  
pp. 399-400 ◽  
Author(s):  
Horst Letz
Keyword(s):  
Coherent States ◽  
Evolution Operator

TIME EVOLUTION OF A CENTRAL OSCILLATOR IN HEAT BATH DERIVED BY VIRTUE OF THE IWOP TECHNIQUE

2006 ◽  
Vol 20 (06) ◽  
pp. 295-304 ◽  
Author(s):  
HONG-YI FAN ◽  
XUE-FEN XU
Keyword(s):  
Partition Function ◽  
Energy Conservation ◽  
Time Evolution ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Evolution Operator ◽  
Heat Bath ◽  
Iwop Technique ◽  
Time Evolution Operator ◽  
Central Oscillator

By virtue of the technique of integration within an ordered product of operators we derive the normally ordered expansion of time evolution operator for the case of a central oscillator immersed in a heat bath composed of a large number of oscillators. The time evolution of the system and heat bath into coherent states is discussed based on energy conservation. As a by-product, the partition function of two coupled oscillators is also calculated in this way.

COHERENT EVOLUTION AND TUNNELING CHARGE STEP IN A DRIVEN MESOSCOPIC JOSEPHSON JUNCTION

1999 ◽  
Vol 13 (12n13) ◽  
pp. 391-397
Author(s):  
BIN SHAO ◽  
JIAN ZOU ◽  
QIANSHU LI
Keyword(s):  
Josephson Junction ◽  
Coherent States ◽  
Evolution Operator ◽  
Weak Link ◽  
Vacuum State ◽  
Time Dependent ◽  
Unitary Evolution ◽  
Dc Voltage ◽  
Mesoscopic System ◽  
Charge Tunneling

We consider a circular superconductor with a weak link mesoscopic Josephson junction in the presence of a dc voltage bias. Using the time-dependent perturbated method, we obtain the unitary evolution operator of the mesoscopic junction system and show that an initial vacuum state of the junction can evolve into a class of superposition of coherent states. Further, we show that the charge tunneling through the junction can exhibit step properties in the mesoscopic system.

scholarly journals Lie algebras and generalized thermal coherent states

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750015 ◽  
Author(s):  
Sergio Floquet ◽  
Marco A. S. Trindade ◽  
J. David M. Vianna
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Wigner Function ◽  
Coherent States ◽  
Density Operator ◽  
Coset Space ◽  
Algebraic Formulation ◽  
Quantum Fidelity

In this paper, we developed an algebraic formulation for the generalized thermal coherent states with a thermofield dynamics approach for multi-modes, based on coset space of Lie groups. In particular, we applied our construction on SU(2) and SU(1,[Formula: see text]1) symmetries and we obtain their thermal coherent states and density operator. We also calculate their thermal quantum Fidelity and thermal Wigner function.

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