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We deal with the gap equation in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature $T$ only. We show that the squared gap function is of class $C^2$ on the closed interval…
We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant $g$…
The superconducting energy gap of $\rm Ba_{1-x}K_xBiO_3$ has been measured by tunneling. Despite the fact that the sample was macroscopically single phase with very sharp superconducting transition $T_c$ at 32~$K$, some of the measured…
We construct a BCS-like model that combines nucleonic pairing correlations and possible quartic correlations of alpha-type in a single variational wave function and derive corresponding gap equations. In the approximation of large…
We investigate a Bose gas with finite-range interaction using a scheme to eliminate unphysical processes in the T-matrix approximation. In this way the corrected T-matrix becomes suitable to calculate properties below the critical…
Temperature-dependent gap equations in the SU(4) model of high-Tc superconductivity are derived and analytical solutions are obtained. Based on these solutions, a generic gap diagram describing the features of energy gaps as functions of…
We review the non-zero temperature relaxational dynamics of quantum systems near a zero temperature, second-order phase transition. We begin with the quantum Ising chain, for which universal and exact results for the relaxation rates can be…
According to the BCS model the probability of filling of pair electron states vk2 as a function of kinetic energy is smeared i.e. is not a step function. This means that part of energy of connection through virtual phonons is consumed to…
For a superconductor to be able to receive an external magnetic field, there must be a vacant energy state in the superconductor to receive the energy associated with the field. For a small range of energies near that of the critical…
We consider two bosonic atoms interacting with a short-range potential and trapped in a spherically symmetric harmonic oscillator. The problem is exactly solvable and is relevant for the study of ultra-cold atoms. We show that the energy…
By applying the particle-number projection to the finite-temperature BCS theory, the $S$-shaped heat capacity, which has recently been claimed to be a fingerprint of the superfluid-to-normal phase transition in nuclei, is reexamined. It is…
Atomic nuclei and nano-scale metallic grains are in the crossover regime of pairing correlations between the bulk limit, where the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity is valid, and the fluctuation-dominated regime,…
Three band crossings can arise in three dimensional quantum materials with certain space group symmetries. The low energy Hamiltonian supports spin $\textit{one}$ fermions and a flat band. We study the pairing problem in this setting. We…
Precise measurements of the thermodynamic critical field ($B_{\rm c}$) in type-I noncentrosymmetric superconductor BeAu were performed by means of the muon-spin rotation/relaxation technique. The temperature evolution of $B_{\rm c}$ can not…
This thesis presents a set of studies on atomic systems where quantum effects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics. First of all, we have studied the prospects…
Predictions for the chemical potential and the excitation gap recently obtained by our diagrammatic theory for the BCS-BEC crossover in the superfluid phase are compared with novel Quantum Monte Carlo results at zero temperature now…
We study finite-temperature properties of a two-dimensional superfluid made of ultracold alkali-metal atoms in the BCS-BEC crossover. We investigate the region below the critical temperature $T_{BKT}$ of the Berezinskii-Kosterlitz-Thouless…
In a prior study of the boron isotope effect on the transition temperature ($T_c$) of $R$Ni$_2$B$_2$C ($R$ = Y, Lu) system, a positive isotope effect was observed, e.g., $T_{c}(^{10}B)> T_{c}(^{11}B)$. BCS theory predicts that the…
Quantum energy transfer in a chain of two-level (spin) units, connected at its ends to two thermal reservoirs, is analyzed in two limits: (i) In the off-resonance regime, when the characteristic subsystem excitation energy gaps are larger…
Recent experiments with ultracold fermionic atoms in optical lattices have provided a tuneable and clean realization of the attractive Hubbard model (AHM). In view of this, several physical properties may be thoroughly studied across the…