scholarly journals Effective Hamiltonian near insulator-superfluid phase transitions

2006 ◽  
Vol 73 (3) ◽  
Author(s):  
Fei Zhou
Keyword(s):  
Phase Transitions ◽  
Effective Hamiltonian ◽  
Superfluid Phase

scholarly journals Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
A. I. Sokolovsky
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
General Formula ◽  
Correlation Functions ◽  
Nonequilibrium Thermodynamic ◽  
Microscopic Theory ◽  
Effective Hamiltonian ◽  
Equilibrium Fluctuations ◽  
Thermodynamic Potentials ◽  
Definition Of

Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed. In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered. A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

Optical Superfluid Phase Transitions and Trapping of Polariton Condensates

2013 ◽  
Vol 110 (18) ◽  
Author(s):  
P. Cristofolini ◽  
A. Dreismann ◽  
G. Christmann ◽  
G. Franchetti ◽  
N. G. Berloff ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Superfluid Phase

scholarly journals Superfluid Phase Transitions in Dense Neutron Matter

2001 ◽  
Vol 87 (3) ◽  
Author(s):  
V. A. Khodel ◽  
J. W. Clark ◽  
M. V. Zverev
Keyword(s):  
Phase Transitions ◽  
Neutron Matter ◽  
Superfluid Phase

scholarly journals Calculation of nonequilibrium thermodynamic potential of Bose system near the condensation point

2018 ◽  
Vol 26 (2) ◽  
pp. 7-16
Author(s):  
K. M. Haponenko ◽  
A. I. Sokolovsky
Keyword(s):  
Perturbation Theory ◽  
Phase Transitions ◽  
Thermodynamic Potential ◽  
Landau Theory ◽  
Nonequilibrium Thermodynamic ◽  
Bose Gas ◽  
Bose System ◽  
Effective Hamiltonian ◽  
Thermodynamic Perturbation Theory ◽  
Thermodynamic Perturbation

Bose system of zero spin particles is considered in the presence of the Bose–Einstein condensate in the vicinity of the phase transition point. The system is investigated in the framework of the Bogolyubov model with the separated condensate. In this model an effective Hamiltonian of the system is introduced by replacing condensate creation and annihilation operators in system Hamiltonian by n01/2 where n0 is occupation number of the condensate state. According to Bogolyubov, the grand canonical thermodynamic potential related to the effective Hamiltonian is considered as nonequilibrium thermodynamic potential. In the present paper this potential is investigated as a function of the small  variable n0. With the help of the thermodynamic perturbation theory it is shown that it is expanded in a series over integer powers of n0. This corresponds to the basic idea of the Landau theory of the phase transitions of the second kind. Coefficients at terms of the first and second orders in n0 in the expansion are calculated for Bose gas in the main approximation in small interaction. Calculation of the coefficients at terms of the third and fourth orders needs accounting contributions of the thermodynamic perturbation theory at least of the 4th order and will be done elsewhere. It is established that the results obtained for Bose gas do not fit into the Landau theory of phase transitions of the second kind. Some comments that discuss the situation are given.

Effective Hamiltonian for the ferroelectric phase transitions in KNbO[sub 3]

1998 ◽  
Author(s):  
U. V. Waghmare ◽  
K. M. Rabe ◽  
Henry Krakauer ◽  
Rici Yu ◽  
Cheng-Zhang Wang
Keyword(s):  
Phase Transitions ◽  
Ferroelectric Phase ◽  
Effective Hamiltonian ◽  
Ferroelectric Phase Transitions

Spin and polarisation

2017 ◽  
Author(s):  
Alexey V. Kavokin ◽  
Jeremy J. Baumberg ◽  
Guillaume Malpuech ◽  
Fabrice P. Laussy
Keyword(s):  
Phase Transitions ◽  
Theoretical Model ◽  
Density Matrix ◽  
Spin Dynamics ◽  
Matrix Formalism ◽  
Superfluid Phase ◽  
Density Matrix Formalism ◽  
Exciton Polaritons ◽  
Semiconductor Microcavities ◽  
Optical Phenomena

In this chapter we consider a complex set of optical phenomena linked to the spin dynamics of exciton-polaritons in semiconductor microcavities. We review a few important experiments that reveal the main mechanisms of the exciton-polariton spin dynamics and present the theoretical model of polariton spin relaxation based on the density matrix formalism. We also discuss the polarisation properties of the condensate and the superfluid phase transitions for polarised exciton-polaritons. We briefly address the polarization multistability and switching in polariton lasers. Finally, the optical spin-Hall and spin-Meissner effects are described.

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