131 research outputs found
Evolution of a Bose-Einstein condensate of neutral atoms --- A field theoretical approach
The particle distribution in a Bose condensate under the trapping potential
and its time evolution after switching off the trapping potential suddenly are
calculated. We investigate the problem from the viewpoint of quantum field
theory,using a model of self-interacting neutral boson field. Within the
approximation of retainng the most dominant term in the Hamiltonian after
applying the Bogoliubov replacement, we can calculate analytically the particle
distribution as a function of space and time coordinates.Comment: 4 pages, LaTe
Dynamical properties of the finite-size Dicke model coupled to a thermal reservoir
We investigate the dynamical properties of the finite-size Dicke model
coupled to a photon reservoir in the dispersive regime. The system-reservoir
coupling in our Hamiltonian includes counter-rotating terms, which are relevant
in the strong atom-cavity coupling. Because the dispersive regime is
considered, the dynamics of low-energy states are described sufficiently
accurately within the finite-dimensional subspace of the dressed states. Using
the separation of the time scales between the system and the reservoir, we
derive the Markovian quantum master equation in the subspace without ignoring
the counter-rotating terms. The temporal evolution of the expectation of the
cavity mode shows that the bifurcation of the long-lived state corresponds to
the superradiant transition in the isolated model. The master equation
explicitly gives the steady state solution. The numerical results for the
first-order correlation function on the steady state indicate that the strong
atom-cavity coupling enhances the coherence and softens the dephasing in the
superradiant region.Comment: 17 pages, 5 figure
Extension of Nelson's Stochastic Quantization to Finite Temperature Using Thermo Field Dynamics
We present an extension of Nelson's stochastic quantum mechanics to finite
temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can
show that Ito's stochastic equations for tilde and non-tilde particle positions
reproduce the TFD-type Schr\"odinger equation which is equivalent to the
Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's
stochastic equation have the temperature dependence and the thermal fluctuation
is induced through the correlation of the non-tilde and tilde particles. We
show that our formalism satisfy the position-momentum uncertainty relation at
finite temperature.Comment: 9 page, 2 figure
From superoperator formalism to nonequilibrium Thermo Field Dynamics
Emphasizing that the specification of the representation space or the
quasiparticle picture is essential in nonequilibrium quantum field system, we
have constructed the unique unperturbed representation of the interaction
picture in the superoperator formalism. To achieve it, we put the three basic
requirements (the existence of the quasiparticle picture at each instant of
time, the macroscopic causality and the relaxation to equilibrium). From the
resultant representation follows the formulation of nonequilibrium Thermo Field
Dynamics (TFD). The two parameters, the number distribution and excitation
energy, characterizing the representation, are to be determined by the
renormalization condition. While we point out that the diagonalization
condition by Chu and Umezawa is inconsistent with the equilibrium theory, we
propose a new renormalization condition as a generalization of the on-shell
renormalization on the self-energy which derives the quantum transport equation
and determines the renormalized excitation energy.Comment: 22 pages, no figur
Stability of Symmetry Breaking States in Finite-size Dicke Model with Photon Leakage
We investigate the finite-size Dicke model with photon leakage. It is shown
that the symmetry breaking states, which are characterized by non-vanishing
and correspond to the ground states in the
superradiant phase in the thermodynamic limit, are stable, while the
eigenstates of the isolated finite-size Dicke Hamiltonian conserve parity
symmetry. We introduce and analyze an effective master equation that describes
the dynamics of a pair of the symmetry breaking states that are the degenerate
lowest energy eigenstates in the superradiant region with photon leakage. It
becomes clear that photon leakage is essential to stabilize the symmetry
breaking states and to realize the superradiant phase without the thermodynamic
limit. Our theoretical analysis provides an alternative interpretation using
the finite-size model to explain results from cold atomic experiments showing
superradiance with the symmetry breaking in an optical cavity.Comment: 12 page
Effects of Inelastic Scattering on Tunneling Time in Generalized Nelson's Quantum Mechanics
We analyze the effects of inelastic scattering on the tunneling time
theoretically, using generalized Nelson's quantum mechanics. This
generalization enables us to describe quantum system with optical potential and
channel couplings in a real time stochastic approach, which seems to give us a
new insight into quantum mechanics beyond Copenhagen interpretation.Comment: 25 pages, 10 Postscript figure
Analysis of Particle Transfer by Periodic Lattice Modulation for Ultracold Fermionic Atom Systems in Three Dimensional Optical Lattice
We analyze a ultracold fermionic atom system in a three dimensional optical
lattice with a confinement harmonic potential, using the Hubbard model, and
time-dependent Gutzwiller variational approach for numerical calculation. Our
study is focused on the time evolution of the particle transfer when the
lattice potential is modulated by adding a periodic one. The choice of the
parameters such as the modulation frequency and amplitude and the particle
number affects the particle transfer. We calculate the time evolution of the
variance in the particle distribution, and show its dependence on the
parameters. The lattice modulation turns out to work effectively in order to
control the particle transfer, and will be a useful method in experiments for
fermionic atom systems.Comment: 14pages, 11figure
Formulation for zero mode of Bose-Einstein condensate beyond Bogoliubov approximation
It is shown for the Bose-Einstein condensate of cold atomic system that the
new unperturbed Hamiltonian, which includes not only the first and second
powers of the zero mode operators but also the higher ones, determines a unique
and stationary vacuum at zero temperature. From the standpoint of quantum field
theory, it is done in a consistent manner that the canonical commutation
relation of the field operator is kept. In this formulation, the condensate
phase does not diffuse and is robust against the quantum fluctuation of the
zero mode. The standard deviation for the phase operator depends on the
condensed atom number with the exponent of , which is universal for both
homogeneous and inhomogeneous systems.Comment: 5 pages, 2 figure
Goldstone Theorem, Hugenholtz-Pines Theorem and Ward-Takahashi Relation in Finite Volume Bose-Einstein Condensed Gases
We construct an approximate scheme based on the concept of the spontaneous
symmetry breakdown, satisfying the Goldstone theorem, for finite volume
Bose-Einstein condensed gases in both zero and finite temperature cases. In
this paper, we discuss the Bose-Einstein condensation in a box with periodic
boundary condition and do not assume the thermodynamic limit. When energy
spectrum is discrete, we found that it is necessary to deal with the
Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which
zero-mode creation- and annihilation-operators are replaced with a {\it
c}-number by hand, for satisfying the Goldstone theorem. Furthermore, we
confirm that the unitary inequivalence of vacua in the spontaneous symmetry
breakdown is true for the finite volume system.Comment: Accepted for publication in Ann. Phys., 33page
Canonical Quantization for a Relativistic Neutral Scalar Field in Non-equilibrium Thermo Field Dynamics
A relativistic neutral scalar field is investigated in non-equilibrium thermo
field dynamics. The canonical quantization is applied to the fields out of
equilibrium. Because the thermal Bogoliubov transformation becomes
time-dependent, the equations of motion for the ordinary unperturbed creation
and annihilation operators are modified. This forces us to introduce a thermal
counter term in the interaction Hamiltonian which generates additional
radiative corrections. Imposing the self-consistency renormalization condition
on the total radiative corrections, we obtain the quantum Boltzmann equation
for the relativistic scalar field.Comment: 20 pages, 2 figure
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