International Journal of Modern Physics B

This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase transitions, universal thermodynamics, scaling functions and correlations for a few prototypical exactly solved models, such as the Lieb–Liniger Bose gas, the spin-1 Bose gas with antiferromagnetic spin-spin interaction, the two-component interacting Fermi gas as well as spin-3/2 Fermi gases. We demonstrate that their corresponding Bethe ansatz solutions provide a precise way to understand quantum many-body physics, such as quantum criticality, Luttinger liquids (LLs), the Wilson ratio, Tan's Contact, etc. These theoretical developments give rise to a physical perspective using integrability for uncovering experimentally testable phenomena in systems of interacting bosonic and fermonic ultracold atoms confined to 1D.

A microscopic description of the critical behavior of systems belonging to the universality class of the three-dimensional (3D) Ising model is developed within the collective variables (CV) approach. The higher non-Gaussian approximation (the sextic distribution for the modes of spin-moment density oscillations or the ρ⁶ model) is used. A specific feature of the partition function calculation for an Ising-like system is the inclusion of the correction for the potential averaging. This correction leads to the modified recurrence relations (RR) for the ρ⁶ model and a nonzero critical exponent of the correlation function η. The RR between the coefficients of the effective sextic distributions are written and analyzed. A technique for determining the small critical exponent η is elaborated in the higher non-Gaussian approximation. It is shown that the renormalized critical exponent of the correlation length has a tendency to a reduction in the case when the exponent η is taken into account.

Work functions of Cr/Ni(111), Cr/Ni(100) and Cr/Ni(110) surfaces with different magnetic configurations for Cr atoms in the topmost Cr monolayer are investigated using first-principles methods based on density functional theory. The calculated results reveal that work functions vary with crystal orientations and magnetic configurations. The magnitude of the Cr magnetic moments for the three (111), (100) and (110) surfaces follows a change trend with M_{Cr, Cr/Ni(111)} < M_{Cr, Cr/Ni(100)} < M_{Cr, Cr/Ni(110)}. Altering the magnetic configurations of the systems from an original ground state to an excited one will have the total energy and the Fermi level increase. Consequently, it will give rise to the reduction of the work function for the system. Moreover, the quite favorable variation range (4.92–4.41 eV) of the calculated work functions for Cr/Ni(100) system modulated by spin effect implies that the Cr/Ni(100) system may be a more promising candidate. Our work suggests that changing magnetic configurations can modulate the work functions of magnetic metal gates well.

We investigate the possibility of discrete groups furnishing a kinematic framework for systems whose thermodynamic behavior may be given by nonadditive entropies. Relying on the well-known result of the growth rate of balls of nilpotent groups, we see that maintaining extensivity of the entropy of a nilpotent group requires using a non-Boltzmann/Gibbs/Shannon (BGS) entropic form. We use the Tsallis entropy as an indicative alternative. Using basic results from hyperbolic and random groups, we investigate the genericity and possible range of applicability of the BGS entropy in this context. We propose a sufficient condition for phase transitions, in the context of (multi-) parameter families of nonadditive entropies.

The modern equilibrium statistical mechanics, intended to link microscopic dynamics to thermodynamic laws for macroscopic quantities, is faced with significant difficulties, as applied to the description of the macroscopic properties of real condensed media within wide thermodynamic ranges, including the vicinities of the phase transition points. A particular problem is the absence of metastable states in the Gibbs statistical mechanics of the systems composed of finite number of particles. Nevertheless, accordance between equilibrium statistical mechanics and thermodynamics of condensed media is achievable if we take account of the mutual correlation (the feedback) between the microscopic properties of molecules and the macrostate of the corresponding medium. This can be done via usage of the "enhanced" Hamilton operator of the considered many-particle system, which contains some temperature-dependent term(s), and the following introduction of the generalized equilibrium distribution over microstates. For illustration of the reasonableness of the proposed approach and of its practical availability in the applications to computing the macroscopic characteristics of condensed media, a cell model of melting/crystallization and metastable supercooled liquid for a water-like medium is presented.

The stationary Wigner functions (WFs) have been calculated for particles evolving in a quartic double-well potential V(x) = ax²/2+bx⁴/4(a < 0 and b > 0), at temperature T. In the high temperature limit, the results totally agree with those obtained using Wigner's perturbative method of deriving quantum corrections to the classical distribution function. Comparison with the perturbative approach allows one to establish the range of applicability of the latter. For illustration, the second moments of the position and momentum have been calculated for the double-well potential. Furthermore, the time-evolution of the WFs for a state initially located at one of the wells has been also investigated to show the tunneling effect.

Polycrystalline La_0.93Sb_0.07MnO₃ ceramics were synthesized using solid-state reaction method. The samples were sintered at different temperatures ranging from 1100°C to 1200°C. It is observed that microstructural, transport and magnetic properties of La_0.93Sb_0.07MnO₃ compounds strongly depend on sintering temperatures (T_S). With T_S increasing, the degree of lattice distortion has been weakened, the grain size has become larger and grain boundaries have decreased. Furthermore, the resistivity was reduced, and metal–insulator transition temperature was enhanced; the saturation magnetization per unit mass has decreased with T_S increasing. These effects of different T_S on physical properties can be explained by the structure distortion and grain boundary contributions for La_0.93Sb_0.07MnO₃ compounds.

In this paper, for the first time, we have used a more precise Hamiltonian matrix based on first nearest neighbor (1NN) and third nearest neighbor (3NN) carbon–carbon interactions to simulate carbon nanotube field effect transistors (CNTFETs). By taking the interactions with more distant neighbors into account, an improvement in tight-binding picture is gained. A self-consistent solution of Schrodinger equation based on nonequilibrium Green's function (NEGF) formalism coupled to a two-dimensional Poisson's equation for treating the electrostatics of the device has been employed to simulate CNTFETs. A tight-binding Hamiltonian with an atomistic (p_z orbitals) mode space basis in the ballistic limits has been used to describe the carbon nanotube (CNT) region. Simulations show that in the presence of 3NN, the energy bandgap of the CNT decreases and consequently the simulated device has lower threshold voltage compared to a simulated device with just 1NN. Short channel effects study demonstrates that neglecting 3NN underestimates the subthreshold swing and overestimates ON/OFF current ratio. All these investigations show that for simulating a CNTFET more precisely, the 3NN interactions can be taken into account in addition to the 1NN.

We propose a framework to describe topological phases with global internal symmetries. This involves embedding the phase of interest into an intrinsic topological-order. Such an embedding is related to the physics of anyon condensation, although no physical condensation actually occurs here. Crucial physical properties of the symmetric phase, such as edge states and global charges of anyons are easily recovered from the embedding. The framework naturally reproduces all phases that are currently known in 2+1 d, and potentially provides a complete classification of symmetric topological phases in 2+1 d. We illustrate our idea with simple examples.