PAIRING OF HOLES INDUCED BY MAGNETIC INTERACTIONS

1988 ◽  
Vol 02 (05) ◽  
pp. 803-810
Author(s):  
D. Schmeltzer
Keyword(s):  
Critical Temperature ◽  
Hole Concentration ◽  
Magnetic Interaction ◽  
Magnetic Interactions ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Many Body ◽  
Large Hole ◽  
The Many ◽  
Bose Einstein

We consider a planar Hubbard model with three sites per primitive cell. This model is mapped into a magnetic Hamiltonian. The charged holes interact via the magnetic interaction. The effect of this interaction is to create a magnetic background for the holes. Defining new quasi-particles we find that the many-body interaction becomes attractive and gives rise to conventional superconductivity. At large hole concentrations the critical temperature is determined by the antiferromagnetic exchange between copper-copper. In addition, the Increase of hole concentration reduces the exchange coupling which vanishes at some critical values. At small hole concentrations the critical temperature is determined by the Bose Einstein condensation temperature.

scholarly journals Beyond mean-field dynamics in closed and open bosonic systems

2013 ◽  
Author(s):  
Γεώργιος Κορδάς
Keyword(s):  
Mean Field ◽  
Einstein Condensation ◽  
Many Body ◽  
Practical Applications ◽  
Body Dynamics ◽  
Systematic Development ◽  
The Many ◽  
Bose Einstein ◽  
State Path ◽  
Present Thesis

The present thesis is devoted to the dynamics in open or closed manybodybosonic systems, with the use of beyond mean-eld methods.In the rst part, inspired by the state-of-the-art experiments, we study thedynamics of a Bose-Einstein condensation which is loaded in an optical latticewith localized loss channels for the atoms. We prove that the particularform of the dissipation can help us to control the many-body dynamics. Theloss allows the local manipulation of the system's coherence properties andcreates attractive xed points in the classical (mean-eld) phase space. Wepredict the dynamical creation of stable nonlinear structures like discretebright and dark solitons. Furthermore, for specic initial states, the systemsproduces highly entangled and long-living states, which are of high relevancefor practical applications. The rst part of this thesis ends with the study ofnon-equilibrium bosonic transport across optical one-dimensional lattices.In the second part, we present techniques for bosonic many-body systemswhich are based on path integrals. We analyze the Bose-Einstein condensationphenomenon by using tools from quantum information theory and eldtheory. Finally, we introduce a coherent state path integral formalism inthe continuum, which allows us the systematic development of approximatemethods for the study of bosons in optical lattices.

scholarly journals Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

2011 ◽  
Vol 369 (1946) ◽  
pp. 2779-2799 ◽  
Author(s):  
Michael M. Scherer ◽  
Stefan Floerchinger ◽  
Holger Gies
Keyword(s):  
Scattering Length ◽  
Einstein Condensation ◽  
Many Body ◽  
Derivative Expansion ◽  
Functional Renormalization Group ◽  
Bose Einstein Condensation ◽  
Fermionic Atoms ◽  
Large Length ◽  
The Many ◽  
Bose Einstein

We review the functional renormalization group (RG) approach to the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation (BCS–BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

QUANTUM KINETIC THEORY FOR A BOSE-EINSTEIN CONDENSED ALKALI GAS

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1641-1650
Author(s):  
M. J. HOLLAND ◽  
J. COOPER ◽  
R. WALSER
Keyword(s):  
Quantum Correlations ◽  
Point Of View ◽  
Einstein Condensation ◽  
Theoretical Point ◽  
Equilibrium System ◽  
Many Body ◽  
Effective Interactions ◽  
Dilute Gas ◽  
The Many ◽  
Bose Einstein

The most salient features of the Bose-Einstein condensation of a magnetically confined alkali vapor is the diluteness of the gas and the extremely weak effective interactions. From a theoretical point of view, the interesting aspect is the potential formulation of the many-body quantum theory for a non-uniform and potentially non-equilibrium system founded entirely on microscopic physics. The crucial postulate is the rapid attenuation of many particle quantum correlations in the dilute system which can be motivated from universal considerations. In principle, it will be possible to provide direct comparison between theory and experiment over all temperature scales with no phenomenological parameters — a challenge facing the theoretical community in the near future. The dilute gas experiments provide an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems, with the single particle microscopic physics described in quantum optics and laser physics.

scholarly journals The Superconducting Critical Temperature

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 911
Author(s):  
Mike Guidry ◽  
Yang Sun ◽  
Lian-Ao Wu
Keyword(s):  
Critical Temperature ◽  
Dynamical Symmetry ◽  
Many Body ◽  
Unconventional Superconductors ◽  
The Many ◽  
Pair Coupling ◽  
Intrinsic Strength ◽  
Superconducting Transitions

Two principles govern the critical temperature for superconducting transitions: (1) intrinsic strength of the pair coupling and (2) the effect of the many-body environments on the efficiency of that coupling. Most discussions take into account only the former, but we argue that the properties of unconventional superconductors are governed more often by the latter, through dynamical symmetry relating to normal and superconducting states. Differentiating these effects is essential to charting a path to the highest-temperature superconductors.

λ-Transition to the Bose-Einstein Condensate

1995 ◽  
Vol 50 (10) ◽  
pp. 921-930 ◽  
Author(s):  
Siegfried Grossmann ◽  
Martin Holthaus
Keyword(s):  
Heat Capacity ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Harmonic Oscillator Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Analytical Expressions ◽  
Grand Canonical

Abstract We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statis­tics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of TV atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N-1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discon­tinuous at the onset of condensation; the magnitude of the jump is about 6.6 N k. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-AT-corrections, and checked against numerical computations.

scholarly journals Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1342
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Infinite Number ◽  
Mean Field ◽  
Solvable Model ◽  
Time Dependent ◽  
Angular Momentum Operator ◽  
Many Body ◽  
The Many ◽  
Bose Einstein ◽  
Number Of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

A MODEL OF BOSE–EINSTEIN CONDENSATION WITH ITINERANT AND LOCALIZED STATES

2005 ◽  
Vol 19 (21) ◽  
pp. 1011-1034
Author(s):  
FUXIANG HAN ◽  
ZHIRU REN ◽  
YUN'E GAO
Keyword(s):  
Critical Temperature ◽  
Anderson Model ◽  
Localized States ◽  
Mean Field Approximation ◽  
Einstein Condensation ◽  
Model Parameters ◽  
Zeroth Order ◽  
Energy Bands ◽  
Bose Einstein Condensation ◽  
Bose Einstein

We propose a model that includes itinerant and localized states to study Bose–Einstein condensation of ultracold atoms in optical lattices (Bose–Anderson model). It is found that the original itinerant and localized states intermix to give rise to a new energy band structure with two quasiparticle energy bands. We have computed the critical temperature Tc of the Bose–Einstein condensation of the quasiparticles in the Bose–Anderson model using our newly developed numerical algorithm and found that Tc increases as na3 (the number density times the lattice constant cubed) increases according to the power law Tc≈18.93(na3)0.59 nK for na3<0.125 and according to the linear relation Tc≈8.75+10.53na3 nK for 1.25<na3<12.5 for the given model parameters. With the self-consistent equations for the condensation fractions obtained within the Bogoliubov mean-field approximation, the effects of the on-site repulsion U on the quasiparticle condensation are investigated. We have found that, for values up to several times the zeroth-order critical temperature, U enhances the zeroth-order condensation fraction at intermediate temperatures and effectively raises the critical temperature, while it slightly suppresses the zeroth-order condensation fraction at very low temperatures.

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