Bardeen-Cooper-Schrieffer theory of finite-size superconducting metallic grains

We study finite-size effects in superconducting metallic grains and determine the BCS order parameter and the low energy excitation spectrum in terms of the size and shape of the grain. Our approach combines the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements, and corrections to the BCS mean field. In chaotic grains mesoscopic fluctuations of the matrix elements lead to a smooth dependence of the order parameter on the excitation energy. In the integrable case we observe shell effects when, e.g., a small change in the electron number leads to large changes in the energy gap.     

用相对论平均场理论研究近滴线区原子核传统幻数的消失和新幻数的产生

提出了一种从理论上检验壳效应的方法.在考虑了由Bardeen，Cooper和Schrieffer提出的金属超导理论(BCS方法)的相对论平均场理论框架内，通过计算粒子数的涨落，发现涨落的大小和核的壳结构有紧密的关系，进而研究了滴线区一些传统幻数的消失和新幻数的产生. 关键词： 相对论平均场理论 粒子数涨落 幻数 壳效应     

Pairing fluctuations in trapped fermi gases

We examine the contribution of pairing fluctuations to the superfluid order parameter for harmonically trapped atomic Fermi gases in the BCS regime. In the limit of small systems we consider, both analytically and numerically, their space and temperature dependence. We predict a parity effect, i.e., that pairing fluctuations show a maximum or a minimum at the center of the trap, depending on the value of the last occupied shell being even or odd. We propose to detect pairing fluctuations by measuring the density-density correlation function after a ballistic expansion of the gas.     

Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result rigorously confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.     

Mott-insulator transition in a two-dimensional atomic Bose gas

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.     

Colour superconductivity in finite systems

We have studied the effects of finite size on the two flavor colour superconducting state. Since the baryon number in the BCS state is only fixed on average, we have projected the state onto a fixed baryon number. The resulting state has been then projected onto a colour-singlet state, by integrating onto the colour group manifold. The effects of both projections have been evaluated numerically.     

Finite-size effects on the statistics of extreme events in the BTW model

The BTW Abelian sandpile model is a prominent example of systems showing self-organised criticality (SOC) in the infinite size limit. We study finite-size effects with special focus on the statistics of extreme events, i.e., of particularly large avalanches. Not only the avalanche size probability distribution, but also the mutual independence of large avalanches in the critical state is affected by finite-size effects. Instead of a Poissonian recurrencetime distribution, in the finite system we find a repulsion of extreme events that depends on the avalanche size and not on the respective probability. The dependence of these effects on the system size is investigated and some data collapse is found. Our results imply that SOC is an unsuitable mechanism for the explanation of extreme events which occur in clusters.     

On surface properties of a weakly-coupled classical one-component plasma: The size effect in finite systems

The surface properties of a weakly coupled classical one-component plasma of finite size are calculated exactly within the Poisson-Boltzmann (PB) approximation scheme. It is found that the ion density profile and the surface energy for a spherical system show strong size dependence. The surface energy also strongly depends on the position of the hard wall introduced for achieving an appropriate equilibrium ion configuration. These results indicate that the recent Monte Carlo simulation data for a spherical system must be interpreted, at least in the weak-coupling regime, as including substantial size effects and cannot be directly compared with the theoretical calculations for the planar surface. For a slab, on the other hand, such size effects are found to be very small if the hard wall is placed at sufficiently distant position from the surface. The dominant contribution to the surface energy which is omitted in the PB approximation is also estimated by the perturbation calculations.     

Power-law temperature dependence of thermally excited transport in one-dimensional systems from Monte Carlo simulation

We investigate the temperature dependence of electric conductance in one-dimensional (1D) systems with thermally excited electron transport under various bias voltages by using Monte Carlo simulation based on the variable-rang hopping (VRH) formula. We find that the temperature dependence of the transport can show a power law behavior as a result of summation over a large number of electron traveling paths although the hopping intensity in every step in the VRH formula is exponentially dependent on the temperature. This can well explain the temperature dependence of conductance measured in various experiments on 1D systems. Without taking the interaction between electrons into account, we can also merge most of our data onto one “universal curve” suggested from the Luttinger Liquid theory. This indicates that the phonon assisted hoppings in disordered 1D systems play an important role at finite temperatures and can provide a simple and efficient explanation for the experimentally observed behavior.     

Evolution of the vortex state in the BCS-BEC crossover of a quasi two-dimensional superfluid Fermi gas

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional(2D) Fermi superfluid system trapped in an optical lattice potential.Within the framework of mean-field theory,the cooper pair density,the atom number density,and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime.Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime.Meanwhile,the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional(3D) to 2D case.Furthermore,using a simple re-normalization procedure,we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G_c which is obtained as a function of the lattice potential's parameter.Finally,we investigate the vortex core size and find that it grows with increasing interaction strength.In particular,by analyzing the behavior of the vortex core size in both BCS and BEC regimes,we find that the vortex core size behaves quite differently for positive and negative chemical potentials.     

Magnetic behavior of nanoscopic superconductors

The magnetic behavior of nanometer-scale superconducting grains at finite temperature is investigated using the correlated static path approximation to the partition function. In these systems, the field penetration depth is much larger than the spatial dimension and Pauli paramagnetism becomes dominant. It is shown that deviations from both the bulk behavior and the BCS results for fixed number parity become significant due to gap fluctuations, which lead to appreciable pairing effects in the spin magnetization and susceptibility beyond the BCS critical fields or sizes. Differences between even and odd systems are also discussed.     

Probing Shell Correction at High Spin by Neutron Emission of Doubly Magic Nuclei 208pb and 132Sn

Shell effects in particle emission for two doubly magic nuclei 132 Sn and 208 Pb were studied in the framework of Smoluchowski equation taking into account temperature and spin-dependent shell correction. It is shown that the shell effects in the enission of pre-scission neutrons are sensitive to the spin dependence of the shell correction at a moderate excitation energy. Therefore, we propose to use neutron multiplicity as an observable to probe the shell correction at high spins.     

Bragg scattering of cooper pairs in an ultracold Fermi gas

We present a theoretical treatment of Bragg scattering of a degenerate Fermi gas in the weakly interacting BCS regime. Our numerical calculations predict correlated scattering of Cooper pairs into a spherical shell in momentum space. The scattered shell of correlated atoms is centered at half the usual Bragg momentum transfer, and can be clearly distinguished from atoms scattered by the usual single-particle Bragg mechanism. We develop an analytic model that explains key features of the correlated-pair Bragg scattering, and determine the dependence of that scattering on the initial pair correlations in the gas.     

Pairing in doped inversion-symmetric Weyl semimetals: a finite temperature analysis from Thouless criterion

In doped Weyl semimetal with inversion symmetry, the two pairing states, i.e., the zero momentum BCS pairing and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing are possible in principle. In this paper we use the standard Thouless criterion for the onset of pairings to investigate the leading pairing instability at the finite temperature. Our results suggest that both BCS and FFLO instabilities are possible depending on the on-site attractive interaction. The competition between the BCS pairing and FFLO pairing is driven by the mutual suppression between density of state near the Fermi surface and finite energy band structure in the whole Brillouin zone. For small and intermediate interaction, the former dominates and supports BCS pairing, while for strong interaction, the latter wins and favors FFLO pairing. We expect our results at the finite temperature can provide some important message to identify the true ground state.     

Probing Shell Correction at High Spin by Neutron Emission of Doubly Magic Nuclei 208Pb and 132Sn

Shell effects in particle emission for two doubly magic nuclei ^132Sn and ^208pb were studied in the framework of Smoluchowski equation taking into account temperature and spin-dependent shell correction. It is shown that the shelle ffects in the emission of pre-scission neutrons are sensitive to the spin dependence of the shell correction at a moderate excitation energy. Therefore, we propose to use neutron multiplicity as an observable to probe the shell correction at high spins.     

Angular momentum and energy dependence of fission andn,p,4He emission from194Hg compound nucleus

Spin and temperature dependence of the fission and particle emission is studied for¹⁹⁴Hg. The compound nucleus is described using the Strutinsky shell correction approach extended for finite angular momenta and temperature. The shell corrections to the potential energy, free energy and the angular momentum are calculated using the Woods-Saxon average field. Results are compared with the experimental data and show a good qualitative agreement. It is found that the inclusion of the shell effects is necessary to understand the decay properties of¹⁹⁴Hg even for temperatures as high as 1.5–2.0 MeV.     

Analytical results for the electronic shell structure in mesoscopic systems: Balian-Bloch type theory for spheres,discs, rings and anti-dot lattices

The electronic shell structure resulting from the interference of closed orbital paths is determined for mesoscopic systems like spherical clusters, discs and rings by extending the semiclassical theory of Balian and Bloch. Analytical results for the shell structure in the density of states are obtained. Thus, the dependence of the shell structure on dimension, size and geometry and potential of the mesoscopic system and on an external magnetic field can be studied systematically. Comparison of the semiclassical results and those of quantum mechanical calculations permits analysis of typical quantum mechanical effects and shows the validity of the semiclassical theory. Our results should stimulate new experiments, can be used to calculate oscillations in the binding-energy, ionization-potential, and can be applied to analyze oscillations in the electronic density of states of quantum dot systems like anti-dot lattices.     

Variational wavefunction for multi-species spinful fermionic superfluids and superconductors

We introduce a new fermionic variational wavefunction, generalizing the Bardeen–Cooper–Schrieffer (BCS) wavefunction, which is suitable for interacting multi-species spinful systems and sustaining superfluidity. Applications range from quark matter to the high temperature superconductors. A wide class of Hamiltonians, comprising interactions and hybridization of arbitrary momentum dependence between different fermion species, can be treated in a comprehensive manner. This is the case, as both the intra-species and the inter-species interactions are treated on equally rigorous footing, which is accomplished via the introduction of a new quantum index attached to the fermions. The index is consistent with known fermionic physics, and allows for heretofore unaccounted fermion–fermion correlations. We have derived the finite temperature version of the theory, thus obtaining the renormalized quasiparticle dispersion relations, and we discuss the appearance of charge and spin density wave order.     

A study of particle number fluctuation under BCS theory

Particle number fluctuations in BCS theory are studied with the relativistic mean-field theory and the shell effects of particle number fluctuations are first discovered. By analyzing the relative errors of the particle number fluctuations, we find that the particle number fluctuations are relevant with the odd-even character. We later apply this method to the examination of the new shell structure, showing that N = 184 for the neutron is indeed a new closed shell.     

Superconductivity in Hubbard models coupled to non-fermionic degrees of freedom

We explore the consequences of coupling between repulsive Hubbard models and Bosonic or spin degrees of freedom. In the regime where the characteristic energy of the non-fermionic part is large compared to the characteristic energy of the Fermions, the effective Hamiltonian corresponds to a generalized attractive Hubbard model. Superconducting properties are then calculated within the BCS scheme including the finite size dependence of correlation functions functions characterizings-wave pairing.