Husimi function and phase-space analysis of bilayer quantum Hall systems at ν = 2/λ

The entropy of an electronic system is defined in terms of the Husimi function, a nonnegative distribution function in phase space. The Husimi function is calculated by maximizing the entropy subject to the constraints that the Husimi function give a Gaussian convolution of the desity when integrating over the momentum coordinates and that its second moment with respect to momentum give a sum of Gaussian convolutions of the density and the kinetic energy density. The result is compared with the Wigner function. Equations are given for calculating the density matrix from the Husimi function. The resulting equation for the exchange energy requires a difficult numerical integration. An alternate method is used to obtain the density matrix from an approximate partially collapsed Husimi matrix that gives the maximum entropy Husimi function as its diagonal. The results are exact for the harmonic oscillator ground state. Exchange energies calculated for H and the He isoelectronic series through C+4 show slight improvements over those calculated using a maximum entropy Wigner function.

For the representation of eigenstates on a Poincare section at the boundary of a billiard different variants have been proposed. We compare these Poincare Husimi functions, discuss their properties, and based on this select one particularly suited definition. For the mean behavior of these Poincare Husimi functions an asymptotic expression is derived, including a uniform approximation. We establish the relation between the Poincare Husimi functions and the Husimi function in phase space from which a direct physical interpretation follows. Using this, a quantum ergodicity theorem for the Poincare Husimi functions in the case of ergodic systems is shown.

This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.

We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev's integral inequality \cite{BA19}. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyonds-parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.

The squeezed light field is a kind of important continuous variable quantum resource.It has wide applications in precision measurement and quantum information processing.Quantum storage is the foundations of quantum repeater and long distance quantum communication,and alkali metal atoms are an ideal quantum storage medium due to long ground state coherent time. With the rapid development of quantum storage technology in atomic medium,the preparation of the squeezed light which resonates with alkali metal atoms has become one of the research hotspots in the field of quantum information.In this paper,we report the generation of squeezed vacuum at 795 nm (resonant on the rubidium D1 transition line) by using an optical parametric oscillation based on a periodically poled KTiOPO4 crystal. The generated squeezed light field is detected by a balanced homodyne detector,and the squeezing of-3 dB and anti-squeezing of 5.8 dB are observed at a pump power of 45 mW.By using a maximum likelihood estimation,the density matrix of the squeezed light field is reconstructed.The time-domain signals from the balanced homodyne detector are collected to acquire the noise distribution of the squeezed light under different phase angles.The likelihood function is established for the measured quadrature components.An identity matrix is chosen as an initial density matrix,and the density matrix of the squeezed field is obtained through an iterative algorithm.The diagonal elements of the density matrix denote the photon number distribution,which includes not only even photon number states but also odd photon number states.The occurrence of odd photon number states mainly comes from the system losses and the imperfect quantum efficiency of detector.The Wigner function in phase space is calculated through the density matrix,and the maximum value of the Wigner function is 0.309.The standard deviation of the squeezed component is 64.4% of that of the vacuum state,corresponding to the squeezing degree of-3.8 dB.The standard deviation of the anti-squeezing component is 1.64 times that of the vacuum state,corresponding to the anti-squeezing degree of 4.3 dB.We theoretically calculate the photon number distribution and the Wigner function of the vacuum squeezed field,and compare the results obtained by theoretical calculation with those obtained by maximum likelihood reconstruction.The probability of vacuum state|0 obtained by maximum likelihood reconstruction is greater,and the probability of photon number state|n(n=1,2,) is smaller than the corresponding theoretical calculation results.From the theoretical calculation,the maximum value of Wigner function is 0.231,and the short axis and long axis of noise range deduced from the contours of the Wigner function are larger than the results from the maximum likelihood reconstruction.The possible reasons for the discrepancy are as follows. 1) The phase scanning is nonuniform during the measurement of the quadrature components.2) The low-frequency electronic noise is not completely filtered out in the datum acquisition process.3) The datum points of measured quadrature components are not enough.In conclusion,we produce a vacuum squeezed field of 795 nm,and obtain the photon number distribution and the Wigner function in phase space through maximum likelihood estimation and theoretical calculation,respectively.This work will provide an experimental basis for generating the Schrodinger cat state.

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Multi-mode Glauber coherent states (MMGS) as well as Bloch states with zero quasi-momentum, which are a special case of generalized coherent states (GCS), are frequently used to describe condensed phases of bosonic many-body systems. The difference of two-point correlators of MMGS and GCS vanishes in the thermodynamic limit. Using the established expansion of MMGS in terms of GCS, we derive a Fourier-type relation between the (auto-)correlation functions of the two different time-evolved states. This relation reveals that the (auto-)correlation and thus the dynamical free-energy density for the two cases are still different, even in the thermodynamic limit, due to the lack of the U(1) symmetry of the MMGS. Analytic results for the deep lattice model of interacting bosons for increasing filling factors show multiple sharp structures in the dynamical free energy-density of increasing complexity. These are explained using the evolution of Husimi functions in phase space.

We discuss and review recent advances in our understanding of quantum Hall systems where additional quantum numbers associated with spin and/or layer (pseudospin) indices play crucial roles in creating exotic quantum phases. Among the novel quantum phases we discuss are the recently discovered canted antiferromagnetic phase, the spontaneous interlayer coherent phase, and various spin Bose glass phases. We describe the theoretical models used in studying these novel phases and the various experimental techniques being used to search for these phases. Both zero temperature quantum phase transitions and finite temperature phase transitions are discussed. Emphasis in this article is on the recent developments in novel quantum phases and quantum phase transitions in bilayer quantum Hall systems where non-trivial magnetic ground states associated with spontaneous spin symmetry breaking play central role.

We have constructed the Wigner function for the ground state of the hydrogen atom and analysed its variation over phase space. By means of the Weyl correspondence between operators and phase space functions we have then studied the description of angular momentum and resolved a dilemma in the comparison with early quantum mechanics. Finally we have discussed the introduction of local energy densities in coordinate space and demonstrated the validity of a local virial theorem.

The electronic structure and geometrical parameters of ground and low-lying excited states of neptunium mono-, di- and tetracarbides were investigated by relativistic CASSCF/CASPT2 multireference calculations with an all-electron basis set as well as with density functional theory (B3LYP) in conjunction with relativistic pseudopotentials. The CASPT2 calculations were extended with complete active space state interaction calculations in order to include spin–orbit coupling and calculate the absorption electronic spectra. In case of the actinide monocarbides, vibrational frequencies were calculated both for the lowest-energy spin-free and spin–orbit states. For the di- and tetracarbides infrared and Raman spectral characteristics were obtained using DFT calculations. For NpC2, two structures were investigated: the symmetric triangular (Np-C2) structure including an acetylide moiety which was found to be the ground state and the symmetric linear (CNpC) structure. In case of NpC4, fourteen different structures were investigated. The ground state was found to be a planar fan-like structure where neptunium is connected to a bent C 4 moiety. The found structures agree well with the previous results on other actinide carbides (Th, U, Pu, Am). The bonding characteristics of the low-energy structures were analysed on the basis of valence molecular orbitals.

Realization of spinor Bose-Einstein condensate in an optical trap has made it possible to create a variety of topological nontrivial structures, due to the vector character of the order parameter. Recently, artificial spin-orbit coupling in the spinor Bose-Einstein condensate, owing to coupling between the spin and the center-of-mass motion of the atom, provides an unprecedented opportunity to search for novel quantum states. As is well known, the potential well in the Bose-Einstein condensate is adjustable. The toroidal trap is an important model potential because of its simplicity and richness in physics. In particular, the spinor Bose-Einstein condensate under the toroidal trap has brought an ideal platform for studying fascinating properties of a superfluid, such as persistent flow and symmetry-breaking localization. For the case of the spin-orbit-coupled Bose-Einstein condensate, the previous studies of the toroidal trap mainly focused on the two-component or antiferromagnetic case. However, in the presence of a toroidal trap, there remains an open question whether the combined effects of the spin-orbit coupling and rotation can produce previously unknown types of topological excitations in the ferromagnetic Bose-Einstein condensate. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in the toroidal trap. We concentrate on the effects of the spin-orbit coupling and the rotation on the ground states. The numerical results show that in the presence of a toroidal trap, the ground state structure is displayed as half-skyrmion chain with circular distribution. Adjusting the strength of spin-orbit coupling not only changes the number of half-skyrmion in the system, but also controls the symmetry of half-skyrmion with circular distribution. As the rotation frequency increases, the system undergoes the transitions from the plane wave to the half-skyrmion chain with circular distribution, and eventually developing the half-skyrmion phase of triangular lattice. Next, we examine the effect of spin-independent interaction on spin-orbit coupled rotating spinor Bose-Einstein condensate. As the spin-independent interaction increases, the topological defects in the condensate increase due to the variation of the local magnetic order. We also discuss the influence of well shape on the ground state structure. These topological structures can be detected via the time-of-flight absorption imaging technique. The spin-orbit coupled spinor Bose-Einstein condensate in the toroidal trap is an important quantum platform, which not only opens up a new avenue for exploring the exotic topological structures, but also is crucial for realizing the transitions among different ground states. This work paves the way for futureexploring the topological defects and the corresponding dynamical stability in quantum system subjected to the toroidal trap.

A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si 6 ground state

We demonstrate that the energy or quasienergy level spacing distribution in dynamically localized chaotic eigenstates is excellently described by the Brody distribution, displaying the fractional power law level repulsion. This we show in two paradigmatic systems, namely for the fully chaotic eigenstates of the kicked rotator at K = 7, and for the chaotic eigenstates in the mixed-type billiard system (Robnik 1983), after separating the regular and chaotic eigenstates by means of the Poincaré Husimi function, at very high energies with great statistical significance (587654 eigenstates, starting at about 1000000 above the ground state). This separation confirms the Berry-Robnik picture, and is performed for the first time at such high energies.

An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then fluctuations in their energy differences—and therefore the possibility of multiple ground states—are closely related to the stability of their ground states. Here we examine the stability of ground states in two models, one of which is presumed to have a ground state structure that is qualitatively similar to other realistic short-range spin glasses in finite dimensions.

We studied a critical size of copper (Cu) clusters where the electronic effect and the size effect on the ground state structure become weaker. Identification of these transitional clusters thus provides with the means to efficiently determine the ground state structure of large clusters using density functional theory (DFT). Our work indicated that beyond the critical size of the transitional cluster, geometrical effects become important, and the putative global minimum structure obtained from an empirical method can be used as an initial structure to determine the true ground state structure using DFT. Structural evolution of ground states was also presented with an increase in the cluster size. To investigate low-lying structures of Cu, we used a Monte Carlo (MC)-simulated annealing method that employs the aggregate-volume-bias MC algorithm. Incorporated in the MC method is an embedded atom method potential developed by the authors. This search method identified the low-lying structures in an effective manner.