Can Anyon Statistics Explain High Temperature Superconductivity?

In this paper, we find a reasonable explanation of high temperature superconductivity phenomena using Anyon statistics.

     

Ground State Energy of the Two-Component Charged Bose Gas

We continue the study of the two-component charged Bose gas initiated by Dyson in 1967. He showed that the ground state energy for N particles is at least as negative as –CN^7/5 for large N and this power law was verified by a lower bound found by Conlon, Lieb and Yau in 1988. Dyson conjectured that the exact constant C was given by a mean-field minimization problem that used, as input, Foldys calculation (using Bogolubovs 1947 formalism) for the one-component gas. Earlier we showed that Foldys calculation is exact insofar as a lower bound of his form was obtained. In this paper we do the same thing for Dysons conjecture. The two-component case is considerably more difficult because the gas is very non-homogeneous in its ground state.Dedicated to Freeman J. Dyson on the occasion of his 80th birthday©2003 by the authors. This article may be reproduced in its entirety for non-commercial purposes.Work partially supported by NSF grant DMS-0111298, by EU grant HPRN-CT-2002-00277, by MaPhySto – A Network in Mathematical Physics and Stochastics, funded by The Danish National Research Foundation, and by grants from the Danish research council.Work partially supported by U.S. National Science Foundation grant PHY01 39984-A01.     

The Antiferromagnetic Correlations in the Half—Filled Double—Exchange Model at Finite Temperature

We extend a previous result of ours [G.S.Tian,Phys.Rev.B63 (2001) 224413] on the antiferromagnetic spin correlations in the half-filled Hubbard model at finite temperature to the double-exchange model.To overcome the mathematical difficulty cused by the S=3/2 localized spin freedom in this model,we apply both Zener‘s argument and the finite-temperature spin-reflection-positivity method to show rigorously that,at any temperature T,the spin correlations in the half-filled double-exchange model are predominantly antiferromagnetic.This conclusion is completely consistent with the experimental observations and the previous theoretical results by approximate methods.     

Superfluid to Normal Fluid Phase Transition in the Bose Gas Trapped in Two-Dimensional Optical Lattices at Finite Temperature

We develop the Hartree-Fock-Bogoliubov theory at finite temperature for Bose gas trapped in the two-dimensional optical lattice with the on-site energy low enough that the gas presents superfluid properties. We obtain the condensate density as function of the temperature neglecting the anomalous density in the thermodynamics equation. The condensate fraction provides two critical temperature. Below the temperature \(T_{C1}\), there is one condensate fraction. Above two condensate fractions merger up to the critical temperature \(T_{C2}\). At temperatures larger than \(T_{C2}\), the condensate fraction is null and, therefore, the gas is normal fluid. We resume by a finite-temperature phase diagram where three domains can be identified: the normal fluid, the superfluid with one stable condensate fraction and the superfluid with two condensate fractions being unstable one of them.     

Derivation of the Leroux System as the Hydrodynamic Limit of a Two-Component Lattice Gas

The long time behavior of a couple of interacting asymmetric exclusion processes of opposite velocities is investigated in one space dimension. We do not allow two particles at the same site, and a collision effect (exchange) takes place when particles of opposite velocities meet at neighboring sites. There are two conserved quantities, and the model admits hyperbolic (Euler) scaling; the hydrodynamic limit results in the classical Leroux system of conservation laws, even beyond the appearance of shocks. Actually, we prove convergence to the set of entropy solutions, the question of uniqueness is left open. To control rapid oscillations of Lax entropies via logarithmic Sobolev inequality estimates, the symmetric part of the process is speeded up in a suitable way, thus a slowly vanishing viscosity is obtained at the macroscopic level. Following [4, 5], the stochastic version of Tartar–Murat theory of compensated compactness is extended to two-component stochastic models.Supported in part by the Hungarian Science Foundation (OTKA), grants T26176 and T037685.     

The Non-Perturbative Approach to the Infrared Problem in QCD at Finite Temperature

A non-perturbative approach is developed for investigation of the infrared problem in QCD at T ≠ 0 in the ghost-free axial gauge. The problem is solved by using a 3-dimensional theory within the exact Slavnov-Taylor identities and Schwinger-Dyson equations. The system of two non-linear integral equations for the structural functions of the gluon polarization tensor is obtained whose solution determines the infrared behavior of the temperature Green functions in the 4-dimensional QCD. The simplest solution of these equations which is the same as the first term of the perturbation expansion shows the presence of singularities in the gluon propagator at momenta p ∼ g²T, that cannot be eliminated by any choice of the gauge. The infrared instability of QCD at T ≠ 0 caused by these singularities is discussed.     

Lowering Critical Temperature in the Extended Quark Sigma Model at Finite Temperature

A phase transition, a critical temperature, and meson masses are studied in the extended quark sigma model, in which the effective mesonic potential is extended to include eighth-order mesonic interactions. The second derivative of the effective mesonic potential is applied to calculate the effective sigma and pion masses as functions of temperature. We find that the critical temperature assumes a lower value in comparison with that of original quark sigma model. A comparison with recent calculations of lattice QCD is introduced. The behavior of the phase transition remains unchanged when the higher-order mesonic interactions are included. We find that the spontaneous symmetry-breaking condition is necessary to satisfy the Goldstone theorem at low temperatures.     

Single-gap s-Wave superconductivity near the charge-density-wave quantum critical point in CuxTiSe2

The in-plane thermal conductivity kappa of the layered superconductor CuxTiSe2 was measured down to temperatures as low as Tc/40, at x=0.06 near where the charge-density-wave order vanishes. The absence of a residual linear term at T-->0 is strong evidence for conventional s-wave superconductivity in this system. This is further supported by the slow magnetic field dependence, also consistent with a single gap, of uniform magnitude across the Fermi surface. Comparison with the closely related material NbSe2, where the superconducting gap is 3 times larger on the Nb 4d band than on the Se 4p band, suggests that in Cu0.06TiSe2 the Se 4p band is below the Fermi level and Cu doping into the Ti 3d band is responsible for the superconductivity.     

The Finite Temperature Effects on the Coleman Phase Transition in Double Sine-Gordon Model

By means of the finite temperature Gaussian effective potential (FTGEP) method, the (1+1) and (2+1) dimensional quantum double sine-Gordon (DsG) field theories are studied nonperturbatively for finite temperature. The explicitly FTGEP is obtained for both (1+1) and (2+1) dimensional DaG models. The temperature-dependent Coleman phase transition conditions obtained by us would reduce to the known results g_cr² when T→0. The alternative explanation of the Coleman phase transition at finite temperature is that for fixed coupling constantg² there is a critical temperature T_cr (whose value depends ong²) such that the theory becomes unstable when the temperature of the system exceeds the critical value T_cr.     

基于局域密度近似理论下的相互作用有限粒子数费米气体的临界温度研究

我们利用局域密度近似方法,通过计算Bogoliubov-de Gennes(BdG)方程研究了三维谐振子势阱约束下,考虑相互作用的有限粒子数费米气体的临界温度随相互作用强度和系统粒子总数的变化关系。结果表明:在相同的相互作用强度下,系统的临界温度随着粒子总数的增多而升高。在相同粒子数条件下,系统的临界温度随着相互作用强度的增大而升高。这里的结果为实验上进一步探寻有限粒子数下的相互作用多体量子系统的超流态到普通态的临界温度提供了理论依据。     

The Casimir Effect at Finite Temperature in a Six-Dimensional Vortex Scenario

The Casimir effect for parallel plates satisfying the Dirichlet boundary condition in the context of effective QED coming from a six-dimensional Nielsen-Olesen vortex solution of the Abelian Higgs model with fermions coupled to gravity is studied at finite temperature. We find that the sign of the Casimir energy remains negative under the thermal influence. It is also shown that the Casimir force between plates will be weaker in the higher-temperature surroundings while keeps attractive. This Casimir effect involving the thermal influence is still inconsistent with the known experiments. We find that the thermal correction can not compensate or even reduce the modification from this kind of vortex model to make the Casimir force to be in less conflict with the measurements.     

The Pion Form Factor on the Lattice at Zero and Finite Temperature

We calculate the electromagnetic form factor of the pion in quenched lattice QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is used together with the consistently -improved current. We calculate the pion form factor for masses down to m_π = 360 MeV, extract the charge radius, and extrapolate toward the physical pion mass. In the second part, we discuss results for the pion form factor and charge radius at 0.93 T_c and compare with zero temperature results.     

Superconductivity in the palladium-silver-deuterium system

Superconducting transition temperatures up to 16 K have been observed for Pd-Ag alloys charged with deuterium or hydrogen by ion implantation at liquid helium temperatures.     

The Master Equation for Two-Level Accelerated Systems at Finite Temperature

In this work, we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a reservoir, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.     

有限温度下介观L-C电路数-相量子涨落

借助于Weyl量子化方案,我们用数-相量子化观点讨论了有限温度下L-C回路的量子噪声,给出了噪声与温度T的函数关系,从数-相量子化方案还能给出相算符的具体形式及电路的振荡行为。     

Meson Properties at Finite Temperature in the Linear Sigma Model

The meson masses are investigated at finite temperature in the framework of the linear sigma model with an explicit chiral symmetry breaking term. The imaginary-time thermo-field dynamics and effective potential have been used for the calculation of the meson masses. We found that the behavior of the sigma and pion masses at finite temperature is in agreement with previous works. The critical temperature, the order of the phase transition, and the dependence of the meson fields on the temperature are discussed.     

Superconductivity in the alkali metals

At ambient pressure there are 29 elemental superconductors in the periodic table, none of which is an alkali metal. The first alkali metal to become superconducting under high pressure is Cs followed years later by Li. Alkali metals are believed to be exemplary free-electron systems. The fact that an alkali metal becomes superconducting at all is surprising and is a result of the fact that under pressure it shows marked deviations from free-electron behaviour where, counterintuitively, bands narrow and gaps widen. For this reason the alkali metals are among the most interesting systems known to study in high-pressure experiments and superconductivity is one of their most fascinating properties.