Volume 127, Nº 5 (2018)

We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential μ and effective magnetic field h, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length 1/a is negative, positive or zero. Within a Luttinger–Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables T/μ and h/μ. The results indicate that beyond the Clogston–Chandrasekhar limit at (h/μ)_c ≃ 1.09, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of ≃0.03T_F.

Using the linearized version of the time dependent Gross–Pitaevskii equation, we calculate the dynamic response of a Bose–Einstein condensed gas to periodic density and particle perturbations. The zero temperature limit of the fluctuation—dissipation theorem is used to evaluate the corresponding quantum fluctuations induced by the elementary excitations in the ground state. In uniform conditions the predictions of Bogoliubov theory, including the infrared divergency of the particle distribution function and the quantum depletion of the condensate, are exactly reproduced by Gross–Pitaevskii theory. Results are also given for the crossed particle-density response function and the extension of the formalism to nonuniform systems is discussed. The generalization of the Gross–Pitaevskii equation to include beyond mean field effects is finally considered and an explicit result for the chemical potential is found, in agreement with the prediction of Lee–Huang–Yang theory.

Time crystallization is a hallmark of superfluidity, indicative of the fundamental fact that along with breaking the global U(1) symmetry, superfluids also break time-translation symmetry. While the standard discussion of the time crystallization phenomenon is based on the notion of the global phase and genuine condensate, for the superfluidity to take place in two dimensions an algebraic (topological) order is sufficient. We find that the absence of long-range order in a finite-temperature two-dimensional superfluid translates into algebraic time crystallization caused by the temporal phase correlations. The exponent controlling the algebraic decay is a universal function of the superfluid-stiffness-to-temperature ratio; this exponent can be also seen in the power-law singularity of the Fourier spectrum of the AC Josephson current. We elaborate on subtleties involved in defining the phenomenon of time crystallization in both classical-field and all-quantum cases and propose an experimental protocol in which the broken time translation symmetry—more precisely, temporal correlations of the relative phase, with all possible finite-size, dimensional, and quantum effects included—can be observed without permanently keeping two superfluids in a contact.

A monolayer of superfluid Fermi gas can be prepared within an optical dipole trap using the tight confinement along the chosen direction. In this case, Cooper pairs occupy the lowest state corresponding to the motion in the trapping potential. After switching off the trapping potential, the initially two-dimensional gas expands to the three-dimensional space. In the case of unitary s-wave interactions, the dynamics of Fermi gas expansion is treated in the framework of appropriately modified Gross–Pitaevskii equation. It is found that the superfluid gas expands significantly faster than the normal gas, in contrast to the situation characteristic of the initially three-dimensional gas. The available experimental data [P. Dyke et al., Phys. Rev. A 93, 011603 (2016)] are close to the predictions of the model under study.

The properties of a scalar field in equilibrium with its own gravitational field are discussed. The scalar field serves as the wavefunction of a Bose–Einstein condensate in equilibrium at a temperature close to absolute zero. The wavefunction of a laboratory Bose–Einstein condensate satisfies the Gross–Pitaevskii equation. The superheavy objects (most likely black holes) at the centers of galaxies are the subject of applying the theory of gravitating fermion and boson clusters. In contrast to a laboratory experiment, the energy spectrum of gravitating bosons is a functional of the wavefunction for the entire condensate. The very presence of a level depends on its population. In particular, at zero temperature for each level, there is a critical total mass M_cr above which an equilibrium configuration (and, hence, this level) does not exist. The critical mass M_cr increases proportionally to the level number. At M > M_cr, the next level acts as the ground state. The concept of the ground state of a boson system is modified. The radius of the sphere occupied by the condensate also increases proportionally to the level number and, therefore, the density does not grow with increasing condensate mass; as long as the spacing between nearby energy levels is great compared to the temperature, no constraints on the total mass arise. One bunch of bosons at a high quantum level with a large mass is energetically less favorable than several isolated centers, with a condensate at the zeroth quantum level being in each of them.

Solitons and localized dissipative structures are the most natural and well-observed manifestations of nonlinear dynamics of energetically open systems at all scales ranging from the quantum structures to astrophysical objects. Depending on the system parameters and an adequate scaling, these phenomena are successfully described by the equations of Korteweg de Vries, Gross–Pitaevskiy, Kadomtsev–Petviashvili, Ginzburg–Landau, and their modifications. In this paper, we shall discuss formation and dynamics of magnetic solitons observed in the solar atmosphere. In particular, we focus on the highly dynamic environment of sunspot areas vastly populated by magnetic solitons. We discuss the properties of these solitons based on their observed signatures, along with their role in dynamics of overlying corona. The results of quantitative analysis of observational data based on the MHD theory of solitary structures are presented.

The effect of an aerogel with parallel fibers on the temperatures of ³He transition to superfluid phases differing in the l_z projections of the orbital angular momentum on the directions of the fibers is considered. It is shown that at the specular reflection of Fermi excitations of liquid ³He from the fibers, the temperature of transition to the polar phase corresponding to l_Z = 0 remains the same as the temperature of transition to any phase with orbital angular momentum l = 1 in the absence of the aerogel. The temperature of transition into phases with l_z = ±1 turns out to be lower, and there appears to be a finite temperature interval in which only the polar phase is stable. This interval has been determined. The effect of the magnetic (exchange) scattering of Fermi excitations at adsorbed ³He atoms on the temperature of transition of ³He to the superfluid state has been estimated.

The works by Lev Petrovich Pitaevskii are reference points for choosing an interesting research topic. An example is the article [1] which promotes rigorous results in nonequilibrium statistical physics. In present paper, we rigorously prove that a nonequilibrium state, on the average, is a local entropy minimum. This statement corresponds to the “entropy growth” of statistical mechanics and does not violate time reversal symmetry of microscopic motion: the first-order time derivative of the entropy is zero \(\dot {S}\) = 0, while the second order derivative is non-negative \(\ddot {S}\) ≥ 0.

We review the behavior of the entropy per particle in various two-dimensional electronic systems. The entropy per particle is an important characteristic of any many-body system that tells how the entropy of the ensemble of electrons changes if one adds one more electron. Recently, it has been demonstrated how the entropy per particle of a two-dimensional electron gas can be extracted from the recharging current dynamics in a planar capacitor geometry. These experiments pave the way to the systematic studies of entropy in various crystal systems including novel two-dimensional crystals such as gapped graphene, germanene, and silicene. Theoretically, the entropy per particle is linked to the temperature derivative of the chemical potential of the electron gas by the Maxwell relation. Using this relation, we calculate the entropy per particle in the vicinity of topological transitions in various two-dimensional electronic systems. We show that the entropy experiences quantized steps at the points of Lifshitz transitions in a two-dimensional electron gas with a parabolic energy spectrum. In contrast, in doubled-gapped Dirac materials, the entropy per particle demonstrates characteristic spikes once the chemical potential passes through the band edges. The transition from a topological to trivial insulator phase in germanene is manifested by the disappearance of a strong zero-energy resonance in the entropy per particle dependence on the chemical potential. We conclude that studies of the entropy per particle shed light on multiple otherwise hidden peculiarities of the electronic band structure of novel two-dimensional crystals.