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Table Of Integrals Series And Products

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

19세기말 애국적 담론과 新小說의 정체성

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound {sup 9}Be{sup +} ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion. {copyright} {ital 1996 The American Physical Society.}

Generation of Non-classical Motional States of a Trapped Atom

When a gas of bosonic particles is cooled below a critical temperature, it condenses into a Bose-Ei…

Bose-Einstein condensation

We study the Casimir effect for a 3D system of ideal Bose gas in a slab geometry with a Dirichlet boundary condition. We calculate the temperature (T) dependence of the Casimir force below and above the Bose–Einstein condensation temperature (Tc). At T ≤ Tc the Casimir force vanishes as . For T Tc it weakly depends on temperature. For T Tc it vanishes exponentially. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of . At finite temperatures the Casimir force for our system depends on .

Bose–Einstein condensation and the Casimir effect for an ideal Bose gas confined between two slabs

We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wave function as well as for the phonon field. We have shown that, the condensate wave function (which obeys the Gross-Pitaevskii equation) is responsible for the mean field part of Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.

Casimir force on interacting Bose-Einstein condensate

We study the Casimir effect for a 3-d system of ideal Bose gas in a slab geometry with Dirichlet boundary condition. We calculate the temperature($T$) dependence of the Casimir force below and above the Bose-Einstein condensation temperature($T_c$). At $T\le T_c$ the Casimir force vanishes as $[\frac{T}{T_c}]^{3/2}$. For $T\gtrsim T_c$ it weakly depends on temperature. For $T\gg T_c$ it vanishes exponentially. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of $\hbar$. At finite temperatures the Casimir force for our system depends on $\hbar$.

https://arxiv.org/pdf/cond-mat/0702215.pdf

Bose-Einstein condensation and Casimir effect for ideal Bose Gas confined between two slabs

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (Tc) the Casimir force for this non-interacting system decreases with temperature (T) and at $T\gtrsim T_c$
 , it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

We have presented an analytic theory for the Casimir force on a Bose–Einstein condensate which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wavefunction as well as for the phonon field. We have shown that the condensate wavefunction (which obeys the Gross–Pitaevskii equation) is responsible for the mean field part of the Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.

Shyamal Biswas

Papers

Bose–Einstein condensation and the Casimir effect for an ideal Bose gas confined between two slabs

Casimir force on interacting Bose-Einstein condensate

Bose-Einstein condensation and Casimir effect for ideal Bose Gas confined between two slabs

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

Casimir force on an interacting Bose–Einstein condensate