Statistical mechanics of flux lines in high-T c superconductors

A theory of the entangled flux liquids which arise in the new high-T _c superconductors is reviewed. New physics appears because of the weak interplanar couplings and high critical temperatures in these materials. Flux line wandering melts the conventional Abrikosov flux lattice, and leads to an entangled vortex state whose statistical mechanics is closely related to the physics of interacting bosons in two dimensions. The phase diagram as a function of magnetic field and temperature is discussed, and it is argued that an entangled vortex liquid appears just aboveH _c1 at all nonzero temperatures. The decay of vortex line correlations in the entangled liquid state is controlled by the superfluid excitation spectrum of the bosons. Line wandering produces drastic changes in theB(H) constitutive relation nearH _c1.     

Kondo effect and mesoscopic fluctuations

Two important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic fluctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic fluctuations; in particular, we consider a small quantum dot coupled to a finite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature T _k which takes into account the mesoscopic fluctuations is a relevant concept: for instance, physical properties are universal functions of T/T _k. Secondly, when the temperature is much less than the mean level spacing due to confinement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-defined single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-field technique, we connect the mesoscopic fluctuations of the quasiparticles in the weak coupling regime to those at strong coupling.     

On the degeneracy of <Emphasis Type="Italic">SU</Emphasis>(3)<Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> topological phases

The ground state degeneracy of an SU(N) _k topological phase with n quasiparticle excitations is a relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any N >2. Here we present the problem in an explicit combinatorial way and analyze the case N = 3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.     

Thermodynamic theory of the equation of state of materials

A universal derivation of the thermodynamic equations on the basis of a combined analysis of the exact relations for any material — the virial theorem, the shock adiabat, and the differential thermodynamic identity relating the thermic and caloric equations of state of matter — is given. This combination makes it possible to reduce the fundamental problem of thermodynamics to a boundary-value problem of mathematical physics. Analytic relations T _s=T(P _s,ρ _s and T _s=T(D,u) are obtained for classical systems. Zh. Tekh. Fiz. 68, 1–9 (October 1998)     

Theory of polar liquids

Two recent contributions to the statistical theory of polar fluids, namely the perturbation theory of Stell, Rasaiah and Narang (SRN) and the meanspherical-approximation (MSA) results of Wertheim, and of Nienhuis and Deutch, are compared and contrasted for the conceptually simple model of hard spheres, diameter R, with central point dipoles, of strength μ (dipolar hard spheres). It is shown that the MSA approach replaces correlation functions which enter correctly into the SRN theory by their low-density limits : to this extent it is unsatisfactory. On the other hand the MSA work does suggest reasons why the naive Padé approximant featuring in SRN theory may be expected to do reasonable justice to the physics of the problem. Numerical comparisons of the excess free-energy (as compared with non-polar hard spheres) as a function of reduced density, ρ* = ρR ³, are given at two temperatures, T* = 2 and T* = 0·25, where T* = kTR ³/μ². Similar curves, for T* = 1 and T* = 0·5, are available from the authors. The gas-liquid (T*, ρ*)-phase boundary is located, near the critical point, on both theories, as are the vapour pressure curves. These are calculated using the Carnahan-Starling equation of state for hard spheres ; and critical comment is made in justification of employing this in the context of MSA results for the excess quantities. The two theories are found to have appreciably different numerical consequences.     

Mutual Chern-Simons theory and its applications in condensed matter physics

In this paper, the mutual Chern-Simons (MCS) theory is introduced as a new kind of topological gauge theory in 2+1 dimensions. We use the MCS theory in gapped phase as an effective low energy theory to describe the Z ₂ topological order of the Kitaev-Wen model. Our results show that the MCS theory can catch the key properties for the Z ₂ topological order. On the other hand, we use the MCS theory as an effective model to deal with the doped Mott insulator. Based on the phase string theory, the t-J model reduces to a MCS theory for spinons and holons. The related physics in high T _c cuprates is discussed.      

Macroscopic approach to the Casimir friction force

The general formula is derived for the vacuum friction force between two parallel perfectly flat planes bounding two material media separated by a vacuum gap and moving relative to each other with a constant velocity v. The material media are described in the framework of macroscopic electrodynamics whereas the nonzero temperature and dissipation are taken into account by making use of the Kubo formulas from non-equilibrium statistical thermodynamics. The formula obtained provides a rigorous basis for calculation of the vacuum friction force within the quantum field theory methods in the condensed matter physics. The revealed v dependence of the vacuum friction force proves to be the following: for zero temperature (T = 0) it is proportional to (v/c)³ and for T > 0 this force is linear in v/c.     

Universality in the length spectrum of integrable systems

The length spectrum of periodic orbits in integrable hamiltonian systems can be expressed in terms of the set of winding numbers {M ₁,…,M _f} on thef-tori. Using the Poisson summation formula, one can thus express the density, Σδ(T−T _M), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable potentials, we explicitly show that the fluctuations are due to quantal energies. Further, their statistical properties are universal and typical of a Poisson process as in the corresponding quantal energy eigenvalues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.     

The statistical theory of nuclear reactions in the limit of isolated resonances II

The random Hamiltonian theory of statistical nuclear reactions is considered in the limit of isolated resonances which means small transmission coefficientsT _e in all open channelse. This generalizes the result of an earlier paper — restricted toT _e =T for alle. A numerical example shows that the present approximation is valid even for unexpectedly large values of theT _e . Thus the formula for the compound nucleus cross sections derived below seems to provide a useful approximation to the exact expression over a large range of possible cases.     

Adsorption of hydrogen in defective carbon nanotube: modelling and consequent investigations using statistical physics formalism

ABSTRACT

Experimental adsorption isotherms of hydrogen in CNT samples (CNT-A, activated CNT-A CNT-B and activated CNT-B) at T?=?77, 87 and 90?K have been fitted using some theoretical model expressions treated by statistical physics through the grand canonical ensemble. The monolayer model with single energy is selected to fit and interpret the experimental data obtained with CNTs. The physico-chemical parameters, interfering in the adsorption process and implicated in the model expressions, could be directly determined from the experimental data through numerical simulation. Three parameters of the model are fitted, namely the number of hydrogen molecule per site n, the interstitial site density N_m and the energetic parameter P_1/2. The evolution of these parameters as function of temperature is plotted and interpreted in relation to adsorption process. Finally, the thermo-dynamic potential functions, which involve in the adsorption mechanism like free enthalpy of Gibbs G_a, internal energy E_int and entropy S_a, are derived by statistical physics calculations from the selected model.