Order Parameter, Mean-Field Theory, and the Ideal Bose Gas

1969 ◽  
Vol 188 (1) ◽  
pp. 522-525 ◽  
Author(s):  
M. Schick ◽  
P. R. Zilsel
Keyword(s):  
Field Theory ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Bose Gas ◽  
Ideal Bose Gas ◽  
The Ideal

CRITICAL DIMENSIONS OF SYSTEMS WITH JOINT MULTICRITICAL AND LIFSHITZ-POINT-LIKE BEHAVIOR

2011 ◽  
Vol 25 (22) ◽  
pp. 1839-1845 ◽  
Author(s):  
ARTEM V. BABICH ◽  
LESYA N. KITCENKO ◽  
VYACHESLAV F. KLEPIKOV
Keyword(s):  
Field Theory ◽  
Critical Phenomena ◽  
Critical Points ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Dimensions ◽  
Lifshitz Point ◽  
The Mean ◽  
Derivatives Of

In this article, we consider a model that allows one to describe critical phenomena in systems with higher powers and derivatives of order parameter. The systems considered have critical points with joint multicritical and Lifshitz-point-like properties. We assess the lower and upper critical dimensions of these systems. These calculation enable us to find the fluctuation region where the mean field theory description does not work.

THE MODE-DEVIATION EFFECT OF TRAPPED SPINOR BOSE GAS BEYOND MEAN FIELD THEORY

2004 ◽  
Vol 18 (09) ◽  
pp. 1339-1349 ◽  
Author(s):  
YAN XU ◽  
DUO-JE JIA ◽  
ZHAO-YANG CHEN ◽  
YUAN GAO ◽  
FA-SHEN LI
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Single Mode ◽  
Bose Gas ◽  
Spin States ◽  
Trapped Atoms ◽  
Atom Number ◽  
The Mean ◽  
Deviation Effect

The deviation effect of spinor mode from the single-mode for a spin-1 Bose gas of trapped atoms is studied beyond the mean field theory. Based on the effective Hamiltonian with nondegenerated level of the collective spin states, the splitting level of the system energy due to the deviation effect has been calculated. For the large condensates of 87 Rb and 23 Na with atom number N>105, the splitting fraction of the energy, arising from the magnetization exhibited by the trapped Bose gas, is found to have a typical order of (10-4~10-8), decreasing as N-2 for 87 Rb and increasing as -N-2 for 23 Na , respectively.

scholarly journals The constructive role of diversity in the global response of coupled neuron systems

2010 ◽  
Vol 368 (1933) ◽  
pp. 5619-5632 ◽  
Author(s):  
Toni Pérez ◽  
Claudio R. Mirasso ◽  
Raúl Toral ◽  
James D. Gunton
Keyword(s):  
Field Theory ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
External Signal ◽  
Global Response ◽  
Diffusive Coupling ◽  
External Modulation ◽  
Collective Response

We study the effect that the heterogeneity present among the elements of an ensemble of coupled excitable neurons has on the collective response of the system to an external signal. We consider two different interaction scenarios, one in which the neurons are diffusively coupled and another in which the neurons interact via pulse-like signals. We find that the type of interaction between the neurons has a crucial role in determining the response of the system to the external modulation. We develop a mean-field theory based on an order parameter expansion that quantitatively reproduces the numerical results in the case of diffusive coupling.

scholarly journals Critical temperature of a trapped Bose gas: Mean-field theory and fluctuations

1997 ◽  
Vol 56 (3) ◽  
pp. 2041-2045 ◽  
Author(s):  
M. Houbiers ◽  
H. Stoof ◽  
E. Cornell
Keyword(s):  
Field Theory ◽  
Critical Temperature ◽  
Mean Field Theory ◽  
Mean Field ◽  
Bose Gas

A QUANTUM SIMULATOR FOR PROBING MOTT LOBES VIA THE AC JOSEPHSON EFFECT

2013 ◽  
Vol 11 (05) ◽  
pp. 1350049
Author(s):  
MING-XIA HUO ◽  
YING LI ◽  
ZHI SONG ◽  
CHANG-PU SUN
Keyword(s):  
Field Theory ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Finite Size ◽  
Weak Field ◽  
Josephson Current ◽  
Theory Approach ◽  
The Mean ◽  
Quantum Simulator

In this paper, we propose to directly detect Mott lobes, i.e. the order parameter 〈a〉, describing the Mott insulator (MI) to superfluid (SF) quantum phase transition of the Bose–Hubbard (BH) model. By weakly coupling the system to an environment in the SF phase, the U(1) symmetry breaking of the system is simulated, and the order parameter can be read from the AC Josephson current between the system and the environment. The relation between the order parameter and the Josephson current is obtained from both the mean-field theory approach and an exact numerical simulation of a finite-size example. Our numerical simulations show that the profile of the order parameter read from the Josephson current is different from it predicted by the mean-field theory, but similar to it in a system whose U(1) symmetry is broken by a weak field proportional to a + a†. This proposal is feasible in optical lattices.

Order parameter and static susceptibility of spin glasses in mean-field theory

1982 ◽  
Vol 1 (2) ◽  
pp. 225-234
Author(s):  
G. Corbelli ◽  
G. Lovecchio ◽  
G. Morandi
Keyword(s):  
Field Theory ◽  
Spin Glasses ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Static Susceptibility

scholarly journals Real-space mean-field theory of a spin-1 Bose gas in synthetic dimensions

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
Hilary M. Hurst ◽  
Justin H. Wilson ◽  
J. H. Pixley ◽  
I. B. Spielman ◽  
Stefan S. Natu
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Bose Gas ◽  
Real Space
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