On the statistical mechanics of elastic manifolds with random interaction

We study the statistical mechanics of D-dimensional elastic manifolds, interacting via randomly distributed forces. It is shown, that this model can be mapped onto the statistical mechanics of disorder-induced roughening of a D-dimensional interface with D transverse degrees of freedom in a disordered medium. The roughness exponent ζ for the lateral deformations is calculated for different kinds of elastic response of the manifolds. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 801–806 (10 December 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as S_t^(D) = N(a D - b lnN) S_\mathrm{t}^{(D)} = N(a D - b \ln N) , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.     

An Effective Mass Theorem for the Bidimensional Electron Gas in a Strong Magnetic Field

We study the limiting behavior of a singularly perturbed Schr?dinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane (x, y) and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr?dinger equations in the plane (x, y), coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator.     

Fermi gas on a lattice in the van Hove limit

We study a Fermi gas with general translation-invariant many-body interactions on a (v3)-dimensional lattice. A complete analysis is given of the perturbative terms up to second order and the program put forward by N. M. Hugenholtz for the derivative of the Boltzmann equation is verified to second order.     

Fermi气体在势阱中的最大囚禁范围与状态方程

在Thomas-Fermi近似条件下,研究了n维广义幂律势阱中Fermi原子气体的最大囚禁范围,给出了n维势阱中气体的实际囚禁体积,导出了状态方程.结果表明,最大囚禁范围和囚禁气体压强不仅与势阱性质有关,也与自由理想Fermi系统的化学势有关.对三维球对称简谐势阱进行了应用,表明在Thomas-Fermi近似有效的前提下,当系统满足条件((kT)/(hω))² ((16π²g)/ 关键词： Fermi气体 n维势阱')" href="#">n维势阱 最大囚禁范围 状态方程     

二维电子体系在高密度下的稳定性

本文计算了高密度的二维电子体系的边缘能(将二维体系沿某一直线解离成两片时,形成单位长度新边缘所需要的能量)。结果发现,当r_ss^(c)(约0.415)时,边缘能变负,从而表明在高密度下,二维电子气的基态有可能发生不稳。我们分别讨论了二维非束缚的电子气和束缚的电子气基态的稳定性,并在一个简化的模型下给出了束缚的电子气基态稳定性的判据。 关键词：     

Electromagnetic quasinormal modes of D-dimensional black holes

Using the monodromy method we calculate the asymptotic quasinormal frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter spacetime.     

Influence of magnetic quantization on the effective electron mass in Kane-type semiconductors

Summary We study the effective electron mass at the Fermi level in Kane-type semiconductors on the basis of fourth order in effective mass theory and taking into account the interactions of the conduction electrons, heavy holes, light holes and split-off holes, respectively. The results obtained are then compared to those derived on the basis of the well-known three-band Kane model. It is found, takingn-Hg_1−x Cd _x Te as an example, that the effective electron mass at the Fermi level in accordance with fourth-order model depends on the Fermi energy, magnetic quantum number and the electron spin respectively due to the influence of band nonparabolicity only. The dependence of effective mass on electron spin is due to spin-orbit splitting parameter of the valence band in three-band Kane model and the Fermi energy due to band nonparabolicity in two-band Kane model. The same mass exhibits an oscillatory magnetic-field dependence for all the band models as expected since the origin of oscillations in the effective mass in nonparabolic compounds is the same as that of the Shubnikov-de Hass oscillations. In addition, the corresponding results for parabolic energy bands have been obtained from the generalized expressions under certain limiting conditions.     

Electromagnetic quasinormal modes of D-dimensional black holes II

By using the sixth order WKB approximation we calculate for an electromagnetic field propagating in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes its quasinormal (QN) frequencies for the fundamental mode and first overtones. We study the dependence of these QN frequencies on the value of the cosmological constant and the spacetime dimension. We also compare with the results for the gravitational perturbations propagating in the same background. Moreover we compute exactly the QN frequencies of the electromagnetic field propagating in D-dimensional massless topological black hole and for the charged D-dimensional Nariai spacetime we calculate exactly the QN frequencies of the coupled electromagnetic and gravitational perturbations.     

Cosmological compactification in Kaluza-Klein model and time-dependent cosmological term

Einstein's equations for the generalized (4+D)-dimensional Robertson-Walker model are solved taking the conformally invariant action for the matter field. Compactification of this model is discussed and the compactification time/compactification mass scale for different values ofD is calculated. The resulting 4-dimensional action for gravity is obtained. It is found that a time-dependent cosmological constant is induced which is very large when the cosmic time is small and very small when the cosmic time is large.     

A physical model for dimensional reduction and its effects on the observable parameters of the universe

We construct a physical model to study the effects of dimensional reduction that might have taken place during the inflationary phase of the universe. The model we propose is a (1 + D)-dimensional (D > 3), nonsingular, spatially homogeneous and isotropic Friedmann model. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. Independent of the details of the process of dimensional reduction, we impose suitable boundary conditions across the transitions and trace the effects of dimensional reduction to the currently observable parameters of the universe. In order to exhibit the cosmological features of the proposed model, we construct a (1 + 4)-dimensional toy model for both closed and open cases of Friedmann geometries. It is shown that in these models the universe makes transition into the lower dimension when the critical length parameter l _4,3, which signals dimensional reduction, reaches the Planck length in D = 3. The numerical models we present in this paper have the capability of making definite predictions about the cosmological parameters of the universe such as the Hubble parameter, age and density.     

Stability of interfaces in a random environment. A rigorous renormalization group analysis of a hierarchical model

We study a hierarchical model of domain walls in aD-dimensional bond disordered Ising model at low temperatures. Using a renormalization group method inspired by the work of Bricmont and Kupiainen for the random field Ising model, we prove the existence of rigid interfaces at low enough temperatures in dimensionsD>3.     

Infrared behaviour of metallic systems in one,two and three dimensions

A simple approximate expression for the electron lifetime() in metals is rederived and discussed for different dimensions. In the 3D-case we get the well known Drude behaviour, i.e. a constant. In one dimension() is strongly frequency-dependent in the IR. The 2D-case is intermediate to the preceding ones. These results are essentially due to the different form of the Fermi surface for an electron gas in one, two and three dimensions.     

Infrared behaviour of metallic systems in one, two and three dimensions

A simple approximate expression for the electron lifetime() in metals is rederived and discussed for different dimensions. In the 3D-case we get the well known Drude behaviour, i.e. a constant. In one dimension() is strongly frequency-dependent in the IR. The 2D-case is intermediate to the preceding ones. These results are essentially due to the different form of the Fermi surface for an electron gas in one, two and three dimensions.     

Particle aggregation versus cluster aggregation in high dimensions

We distinguish two different types of irreversible aggregation-accretion of individual particles and successive aggregation of clusters of comparable size. In aggregation of particles which follow trajectories of fractal dimensionD ₁, we show that physical limits on the aggregation rate impose a lower bound on the fractal dimensionD ₀ of the aggregate. Ind-dimensional space,D ₀{d–D}₁ + 1. Thus aggregation of ballistic particles, withD ₁ = 1, is not fractal. By contrast, cluster aggregates appear to attain a finite, limitingD ₀ in high dimensions. We present a soluble model with this property, and argue that it should agree with Sutherland's binary aggregation model in high dimensions. For this model,D ₀ depends continuously on a parameter; the exponent is not universal.     

Higher dimensional cosmologies

Einstein equations are derived for D-dimensional space-time that spontaneously compactify to the product M⁴ × Π_{i = 1}^α M^d_i in which the metric is taken to be of the generalized Robertson-Walker form. Cosmological solutions for these equations are studied with power law, oscillatory and exponential behaviour for the D-dimensional Einstein-Maxwell, N = 2, D = 10 and N = 1, D = 11 supergravity models. In the Einstein-Maxwell case the presence of a cosmological constant forces the extra dimensions to be static. Nevertheless, it is possible to find solutions with vanishing effective 4 dimensional cosmological constant with an expanding 4-dimensional space-time. In the supergravity models the requirement of having compact extra dimensions restricts the solutions to have expansion only in the 4-dimensional space-time. Matter contribution is added to the energy-momentum tensor in an attempt to find new solutions.     

Quasinormal modes of D-dimensional de Sitter spacetime

We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in D-dimensional de Sitter spacetime (D ≥ 4). We also study the quasinormal modes of a real massive scalar field and compare our results with those of other references.     

The universal sound velocity formula for the strongly interacting unitary Fermi gas

Due to the scale invariance,the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas.For example,the virial theorem between pressure and energy density of the ideal gas P=2E/3V is still satisfied by the unitary Fermi gas.This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation.For comparison,the sound velocities for the ideal Boltzmann,Bose and Fermi gas are also given.Quite interestingly,the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.     

Tensor Network States and Geometry

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure of geodesics in the physical and holographic geometries, respectively; whereas the asymptotic scaling of entanglement entropy is seen to always obey a simple boundary law—that is, again in the relevant geometry. This geometrical interpretation offers a simple and unifying framework to understand the structural properties of, and helps clarify the relation between, different tensor network states. In addition, it has recently motivated the branching MERA, a generalization of the MERA capable of reproducing violations of the entropic boundary law in D>1 dimensions.     

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T _⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T _*, appears through a crossover at temperatures T ∼ T _* > T _⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T ^−α with the exponent α }~ 2/3.