scholarly journals Impurities in a one-dimensional Bose gas: the flow equation approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fabian Brauneis ◽  
Hans-Werner Hammer ◽  
Mikhail Lemeshko ◽  
Artem Volosniev
Keyword(s):  
Mean Field ◽  
Interaction Strength ◽  
Field Approximation ◽  
Flow Equation ◽  
Mean Field Approximation ◽  
Bose Gases ◽  
One Dimensional ◽  
Flow Equations ◽  
Impurity Interaction ◽  
The Mean

A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities[1,2]. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

COLLAPSE OF K-Rb FERMI-BOSE MIXTURES IN OPTICAL LATTICES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5199-5203
Author(s):  
D. M. JEZEK ◽  
H. M. CATALDO
Keyword(s):  
Low Temperature ◽  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
One Dimensional ◽  
Different Types ◽  
The Mean ◽  
Number Of Particles

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

FRÖHLICH'S ONE-DIMENSIONAL SUPERCONDUCTOR WITH PARA-FERMI STATISTICS

1994 ◽  
Vol 08 (19) ◽  
pp. 1195-1200 ◽  
Author(s):  
V. L. SAFONOV ◽  
A. V. ROZHKOV
Keyword(s):  
Density Wave ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Wave State ◽  
One Dimensional ◽  
Fermi Statistics ◽  
The Mean ◽  
A Charge ◽  
Dimensional Crystal

The hypothesis that conduction electrons in a one-dimensional crystal obey para-Fermi statistics is discussed. Thermal properties of Fröhlich's model in the mean-field approximation are calculated within the framework of this hypothesis. It is shown that the temperature of the phase transition to a charge density wave state is greater in a system with parastatistics.

The renormalization group (RG) approach: The critical theory near four dimensions

2021 ◽  
pp. 357-390
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gaussian Approximation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Flow Equations ◽  
Four Dimensions ◽  
The Mean

In Chapter 14, the singular behavior of ferromagnetic systems with O(N) symmetry and short-range interactions, near a second order phase transition has been determined in the mean-field approximation, which is also a quasi-Gaussian approximation. The mean-field approximation predicts a set of universal properties, properties independent of the detailed structure of the microscopic Hamiltonian, the dimension of space, and, to a large extent, of the symmetry of systems. However, the leading corrections to the mean-field approximation, in dimensions smaller than or equal to four, diverge at the critical temperature, and the universal predictions of the mean-field approximation cannot be correct. Such a problem originates from the non-decoupling of scales and leads to the question of possible universality. In Chapter 9, the question has been answered in four dimensions using renormalization theory, and related renormalization group (RG) equations. Moreover, below four dimensions, in an expansion around the mean-field, the most singular terms near criticality can be also formally recovered from a continuum, low-mass φ4 field theory. More generally, following Wilson, to understand universality beyond the mean-field approximation, it is necessary to build a general renormalization group in the form of flow equations for effective Hamiltonians and to find fixed points of the flow equations. Near four dimensions, the flow equations can be approximated by the renormalization group of quantum field theory (QFT), and the fixed points and critical behaviours derived within the framework of the Wilson-Fisher ϵ expansion.

scholarly journals NONLINEAR EFFECT ON THE TRANSMISSION OF LIGHT IN A CAVITY ARRAY

2011 ◽  
Vol 09 (02) ◽  
pp. 677-687
Author(s):  
H. D. LIU ◽  
W. WANG ◽  
X. X. YI
Keyword(s):  
Nonlinear Effect ◽  
Transmission Rate ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Level System ◽  
One Dimensional ◽  
Coherent Transport ◽  
The Mean ◽  
Cavity Array

Taking nonlinear effect into account, we study theoretically the transmission properties of photons in a one-dimensional coupled cavity, the cavity located at the center of the cavity array being coupled to a two-level system. By using the traditional scattering theory and the mean-field approximation, we calculate the transmission rate of photons along the cavities, and discuss the effect of nonlinearity and the cavity-atom coupling on the photon transport. The results show that the cavity-atom couplings affect the coherent transport of photons. The dynamics of such a system is also studied by numerical simulations, the effect of the atom-field detuning and nonlinearity on the dynamics is shown and discussed.

Application of the Mean-Field Approximation to the Magnetic and Superconducting Phases of Quasi-One-Dimensional Metal

2009 ◽  
Vol 152-153 ◽  
pp. 591-594 ◽  
Author(s):  
A.V. Rozhkov
Keyword(s):  
Density Wave ◽  
Spin Density Wave ◽  
Mean Field ◽  
Field Approximation ◽  
High Energy ◽  
Mean Field Approximation ◽  
One Dimensional ◽  
Ordered Phases ◽  
The Mean ◽  
The One

We research under what condition the mean-field approximation can be applied to study ordered phases of quasi-one-dimensional metal. It is shown that the mean-field treatment is indeed permissible provided that it is applied not to the microscopic Hamiltonian (subject to severe one-dimensional high-energy fluctuations), but rather to effective Hamiltonian derived at the dimensional crossover scale. The resultant mean-field phase diagram has three ordered phases: spin density wave, charge density wave, and superconductivity. The density wave orders win if the Fermi surface nests well. Outcome of competition between the intra-chain and inter-chain electron repulsion determines the type (spin vs. charge) of the density wave. The ground state becomes superconducting (with unconventional order parameter) when the nesting is poor. The superconducting mechanism relies crucially on the one-dimensional fluctuations.

The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

Sign in / Sign up

Export Citation Format

Share Document