Condensed Matter

It is shown that in general case may be not correct the statements of [1,2,6-8] that 1) the isochoric heat capacity on the entire thermodynamic surface, including the metastable region of states and the region defined by the spinodal, remains positive and finite except for the critical point, and 2) the isobaric heat capacity becomes negative in the region defined by spinodal.

A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced a set of alternative LDAs constructed from one-dimensional systems of one, two, and three electrons that resemble the HEG within a finite region. We now construct a HEG-based LDA appropriate for spinless electrons in one dimension and find that it is remarkably similar to the finite LDAs. As expected, all LDAs are inadequate in low-density systems where correlation is strong. However, exploring the small but significant differences between the functionals, we find that the finite LDAs give better densities and energies in high-density exchange-dominated systems, arising partly from a better description of the self-interaction correction.

Superfluid phases of 3 He discovered in 1972 opened the new area of the application of topological methods to condensed matter systems. Due to the multi-component order parameter which characterizes the broken SO(3)×SO(3)×U(1) symmetry in these phases, there are many inhomogeneous objects -- textures and defects in the order parameter field -- which are protected by topology and are characterized by topological quantum numbers. Among them there are quantized vortices, skyrmions and merons, solitons and vortex sheets, monopoles and boojums, Alice strings, Kibble-Lazarides-Shafi walls terminated by Alice strings, spin vortices with soliton tails, etc. Most of them have been experimentally identified and investigated using nuclear magnetic resonance (NMR) techniquie, and in particular the phase coherent spin precession discovered in 1984 in 3 He-B by Borovik-Romanov, Bunkov, Dmitriev and Mukharskiy in collaboration with Fomin.

In this work we have obtained a higher-derivative Lagrangian for a charged fluid coupled with the electromagnetic fluid and the Dirac's constraints analysis was discussed. A set of first-class constraints fixed by noncovariant gauge condition was obtained. The path integral formalism was used to obtain the partition function for the corresponding higher-derivative Hamiltonian and the Faddeev-Popov ansatz was used to construct an effective Lagrangian. Through the partition function, a Stefan-Boltzmann type law was obtained.

We present a general method of constructing maximally localized Wannier functions. It consists of three steps: (1) picking a localized trial wave function, (2) performing a full band projection, and (3) orthonormalizing with the Lowdin method. Our method is capable of producing maximally localized Wannier functions without further minimization, and it can be applied straightforwardly to random potentials without using supercells. The effectiveness of our method is demonstrated for both simple bands and composite bands.

When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu-Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy, particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be fewer than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this article, we review recently established formulas for NGMs associated with broken internal symmetries that work equally for relativistic and nonrelativistic systems. We also discuss complexities of NGMs originating from space-time symmetry breaking. In the process we cover many illuminating examples from various context. We also present a complementary point of view from the Lieb-Schultz-Mattis theorem.

We study the coupled dynamics of normal and superfluid components of the superfluid 4 He in the channel considering the counterflow turbulence with laminar normal component. In particular, we calculated profiles of the normal velocity, the mutual friction, the vortex line density and other flow properties and compared them to the case when the dynamic of the normal component is "frozen". We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore coupling, becomes stronger. The commonly measured flow properties also change when the coupling between two components is taken into account.

We have investigated co-directional and contra-directional couplings between spin wave and acoustic wave in one-dimensional periodic structure (magphonic crystal). The system consists of two ferromagnetic layers alternating in space. We have taken into consideration materials commonly used in magnonics: yttrium iron garnet, CoFeB, permalloy, and cobalt. The coupled mode theory (CMT) formalism have been successfully implemented to describe magnetoelastic interaction as a periodic perturbation in the magphonic crystal. The results of CMT calculations have been verified by more rigorous simulations by frequency-domain plane wave method and time-domain finite element method. The presented resonant coupling in the magphonic crystal is an active in-space mechanism which spatially transfers energy between propagating spin and acoustic modes, thus creating propagating magnetoelastic wave. We have shown, that CMT analysis of the magnetoelastic coupling is an useful tool to optimize and design a spin wave - acoustic wave transducer based on a magphonic crystals. The effect of spin wave damping has been included to the model to discuss the efficiency of such a device. Our model shows that it is possible to obtain forward conversion of the acoustic wave to the spin wave in case of co-directional coupling and backward conversion in case of contra-directional coupling.

For helium II inside a rotating cylinder, it is proposed that the formation of vortex lines of the frictionless superfluid component of the liquid is caused by the presence of the rotating quasi-particles gas. By minimising the free energy of the system, the critical value Omega_0 of the angular velocity for the formation of the first vortex line is determined. This value nontrivially depends on the temperature, and numerical estimations of its temperature behaviour are produced. It is shown that the latent heat for a vortex formation and the associated discontinuous change in the angular momentum of the quasi-particles gas determine the slope of Omega_0 (T) via some kind of Clapeyron equation.

The paper analyzes a general case of an equation of state, which is an analytical function at the critical point of the liquid-vapor first order phase transition of pure substance. It is shown that the equality to zero of the first- and second-order partial derivatives of pressure with respect to volume (density) at the critical point is the consequence of the thermodynamic conditions of phase equilibrium. We obtained the relations of critical exponents and amplitudes with parameters of the analytical equation of state. It is shown that the substance with the analytical equation of state can have critical exponents of lattice gas which is equivalent to the two dimensional Ising model. It is shown that the analytical equation of state can take into account the density fluctuations.