Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment

We study the temporal evolution of a central spin-1/2 (qubit) coupled to the environment which is chosen to be a spin-1/2 transverse XY spin chain. We explore the entire phase diagram of the spin-Hamiltonian and investigate the behavior of Loschmidt echo(LE) close to critical and multicritical point(MCP). To achieve this, the qubit is coupled to the spin chain through the anisotropy term as well as one of the interaction terms. Our study reveals that the echo has a faster decay with the system size (in the short time limit) close to a MCP and also the scaling obeyed by the quasiperiod of the collapse and revival of the LE is different in comparison to that close to a QCP. We also show that even when approached along the gapless critical line, the scaling of the LE is determined by the MCP where the energy gap shows a faster decay with the system size. This claim is verified by studying the short-time and also the collapse and revival behavior of the LE at a quasicritical point on the ferromagnetic side of the MCP. We also connect our observation to the decoherence of the central spin.     

Quantum States of a Neutral Massive Fermion with an Anomalous Magnetic Moment in an External Electric Field

The quantum dynamics of a nonrelativistic neutral massive fermion with an anomalous magnetic moment (AMM) is examined in the external electric field of an infinitely long thin homogeneously charged thread in the plane with a normal directed along the thread. The Hamiltonian of the Dirac–Pauli equation for a neutral fermion with AMM is essentially singular in the considered external field and requires a supplementary extension of the definition in order for it to be treated as a self-adjoint quantum-mechanical operator. All one-parameter self-adjoint extensions of the Hamiltonian of the Dirac–Pauli equation in the considered external field are found in the nonrelativistic approximation. The corresponding Hilbert space of squareintegrable functions, including a singularity point of the Hamiltonian, is specified for each self-adjoint extension of the Hamiltonian. The wave functions of free and bound states, as well as discrete energy levels, are determined by the self-adjoint extension method and their correspondence with similar quantities obtained by the physical regularization procedure is discussed. It is shown that energy levels of bound states are simple poles of the scattering amplitude, which should be extended in definition by introducing the self-adjoint extension parameter into it. Expressions for the scattering amplitude and cross-section, depending on the orientation of the initial-state spin of fermion, are obtained.     

Optical anisotropy of InAs/GaSb broken-gap quantum wells

We investigate in detail the optical anisotropy of absorption of linearly polarized light in InAs/GaSb quantum wells grown on GaSb along the [001] direction, which can be used as an active region of different laser structures. The energy level positions, the wave functions, the optical matrix elements, and the absorption coefficients are calculated using the eight-band k · p model and the Burt-Foreman envelope function theory. In these calculations, the Schr?dinger and Poisson equations are solved self-consistently taking the lattice-mismatched strain into account. We find that a realistic Hamiltonian, which has the C _2v symmetry, results in considerable anisotropy of optical matrix elements for different directions of light polarization and different directions of the initial-state in-plane wave vector, including low-symmetry directions. We trace how the optical matrix elements and absorption are modified when spin-orbit interaction and important symmetry breaking mechanisms are taken into account (structural inversion asymmetry, bulk inversion asymmetry, and interface Hamiltonian). These mechanisms result in an almost 100% anisotropy of the absorption coefficients as the light polarization vector rotates in the plane of the structure and in a plane normal to the interfaces.     

Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models

We numerically study the phase structure of two types of triangulated spherical surface models, which includes an in-plane shear energy in the Hamiltonian, and we found that the phase structure of the models is considerably influenced by the presence of the in-plane shear elasticity. The models undergo a first-order collapsing transition and a first-order (or second-order) transition of surface fluctuations; the latter transition was reported to be of second-order in the first model without the in-plane shear energy. This leads us to conclude that the in-plane elasticity strengthens the transition of surface fluctuations. We also found that the in-plane elasticity decreases the variety of phases in the second model without the in-plane energy. The Hamiltonian of the first model is given by a linear combination of the Gaussian bond potential, a one-dimensional bending energy, and the in-plane shear energy. The second model is obtained from the first model by replacing the Gaussian bond potential with the Nambu-Goto potential, which is defined by the summation over the area of triangles.     

Short-time fractional Fourier methods for the time-frequency representation of chirp signals

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.     

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n > 2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses. PACS Number: 05.20.-y, 02.30.Mv, 66.10.-x, 78.70.Nx, 05.60.Cd     

Single-file diffusion of atomic and colloidal systems: asymptotic laws

We present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a particle at position x(t) after time t, when the particle was located at x(0) at t=0, follows a Gaussian distribution in the long-time limit, with variance 2W(t) approximately t(1/2) for overdamped systems and with variance 2W(t) approximately t for classical systems. The asymptotic behavior of the mean-squared displacement, W(t), is shown to be independent of the nature of interactions for homogeneous systems in the fluid state. Moreover, the long-time behavior of self-diffusion is determined by short-time and large-scale collective density fluctuations.     

The Ghirlanda-Guerra Identities

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.     

An exactly solvable model for the large polaron

We present an exactly diagonalizable model Hamiltonian for the large polaron derived by analyzing the variational ansatz by Haga-Larsen (HL) for the Fröhlich Hamiltonian. The lowest energy eigenvalue of the model Hamiltonian for fixed wave numbers reproduces the energy of the variational ansatz by Haga-Larsen and is, therefore, an upper bound with respect to the corresponding energy eigenvalue of the Fröhlich Hamiltonian. This is valid for any momentum which is proven by extending the Haga-Larsen approach. Furthermore, since all integrations can be performed analytically, the model Hamiltonian is easily tractable. The energy eigenvalue spectrum of the model Hamiltonian is studied below and above the phonon-emission threshold. The quality of the model Hamiltonian is determined by the variational ansatz of Haga and Larsen. Incorporating an improved energy-momentum relation, a generalized model Hamiltonian is derived possessing a larger validity range with respect to the coupling strength. Furthermore, a second exactly diagonalizable model Hamiltonian based on improved Wigner-Brillouin perturbation theory due to Warmenbol, Peeters, and Devreese (WPD) is presented. It is briefly demonstrated that one is able to construct all mentioned model Hamiltonians also in the 2D polaron problem. In contrast to the 3D case, where the HL-type model Hamiltonian possesses the higher quality for any momentum, in the 2D case, it works well only for small momenta. For large momenta, only the WPD-type model Hamiltonian describes the energy-momentum relation correctly. We demonstrate the usefulness of the model Hamiltonian concept by exactly calculating the one-electron Green’s function for all mentioned model Hamiltonians and comment why significant advantages of the model Hamilton concept for the treating of low-dimensional systems (planar semiconducting quantum-well structures) can be expected.     

Observation of a topological relaxation mode in microemulsions

We report the observation of two diffusive relaxation modes in a very swollen microemulsion, measured by quasielastic light scattering experiments. In addition to a short-time diffusion process, we observe a long-time diffusive relaxation mode with unusual scaling behavior: the diffusion constant D is an exponential function of the characteristic length scale xi, D~exp(-xi). This observation provides experimental evidence for thermally activated topological relaxation of random fluid phases, as predicted by Milner et al. [J. Phys. (Paris) 51, 2629 (1990)]. We describe the activation energy of such a process by some simple microscopic model for the surfactant layer and give an estimation of the membrane elastic and Gaussian moduli kappa and kappa;, and its spontaneous curvature.     

Analytical model of drift and diffusion of charge carriers in organic light-emitting diodes in the presence of a space charge

A relatively simple analytical model taking into account energy disorder and space charge effects is proposed for calculating the current-voltage characteristics for the monopolar regime of charge transfer in thin layers of disordered organic materials. The dependence of the minimal energy barrier height for injection, for which the space charge effects can be disregarded, is determined as a function of the layer thickness and the Gaussian energy distribution width.     

Laser-induced quadrupoleben quadrupole collisional energy transfer in Xe-Kr

By considering the relative velocity distribution function and multipole expansion interaction Hamiltonian, a three-state model for calculating the cross section of laser-induced quadrupole-quadrupole collisional energy transfer is presented. Calculated results in Xe-Kr system show that in the present system, the laser-induced collision process occurs for ~4 ps, which is much shorter than the dipole-dipole laser-induced collisional energy transfer (LICET) process. The spectrum of laser-induced quadrupole-quadrupole collisional energy transfer in Xe-Kr system has wider tunable range in an order of magnitude than the dipole-dipole LICET spectra. The peak cross section decreases and moves to the quasi-static wing with increasing temperature and the full width at half peak of the profile becomes larger as the system temperature increases.     

Energy shift of photoemission spectra for organics-passivated CdSe nanoparticles: The final-state effect

Size-dependent energy shift of photoemission spectra with respect to bulk sample has been examined for colloidally prepared CdSe nanoparticles with a series of particle sizes. The core-level shifts are well described by a theoretical calculation based on a final-state effect model, whereas an additional initial-state effect due to quantum confinement is required to elucidate the valence-band edge shifts. The results indicate that the interaction between the photohole and the dielectric background in the final state has to be considered in photoemission measurements for organics-passivated nanoparticles. The calculated results in the literature appear to overestimate the initial-state effect compared to our experimental observation.     

Effect of Electron Itineracy on Magnetism of S ＝ 1/2 Ferromagnetic Ising Model

The effect of electron itineracy on the magnetism of S＝1/2 ferromagnetic Ising model is investigated by introducing a hopping term. The electron Green's function method is used to deal with this Hamiltonian. Here emphasis is made on that the magnetization is caused by the difference between the filling of spin-up and spin-down electrons.This concept is in accordance with that of band structure theory. In the zero band width limit, our results are the same as obtained by spin Green's function method. However, our method achieves more detailed physical information. The spontaneous magnetization, Curie temperature, total energy, and specific heat are calculated and investigated in detail by the densities of states. Hopping term depresses the Curie temperature but remains the order-disorder transformation still to be second order transition. Above the transition point, the energy band is the same as that of tight binding system because exchange interaction has no effect anymore. While under the transition point, the energy band splits into two subbands due to exchange interaction.     

Energy Transfer in the Light-Harvesting Complexes of Purple Bacteria

In this paper, we use a nonlinear decohering quantum model to study the initial step of photosynthesis which is an ultrafast transfer process of absorption the sunlight by light-harvesting complexes and electronic excitation transfer to the reaction center(RC). In this decohering model, the Hamiltonian of the system commutes with the systemenvironment interaction. We take B850 ring of light-harvesting complex II(LH-II) in purple bacteria as an example to calculate the efficiency of the energy transfer as a function of time. We find that the environmental noise can make the LH-II have stable energy transfer efficiency over a long time. This is to say that the environmental noise which is the decohering source has advantage of the energy transfer in the process of photosynthesis.     

Interaction of regular and chaotic states

Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of random matrices (GOE), we investigate the interaction of the GOE with regular bound states. The eigenvalues of the latter may or may not be embedded in the GOE spectrum. We derive a generalized form of the Pastur equation for the average Green’s function. We use that equation to study the average and the variance of the shift of the regular states, their spreading width, and the deformation of the GOE spectrum non-perturbatively. We compare our results with various perturbative approaches.     

Variational quantum eigensolvers by variance minimization

The original variational quantum eigensolver (VQE) typically minimizes energy with hybrid quantum-classical optimization that aims to find the ground state. Here, we propose a VQE based on minimizing energy variance and call it the variance-VQE, which treats the ground state and excited states on the same footing, since an arbitrary eigenstate for a Hamiltonian should have zero energy variance. We demonstrate the properties of the variance-VQE for solving a set of excited states in quantum chemistry problems. Remarkably, we show that optimization of a combination of energy and variance may be more efficient to find low-energy excited states than those of minimizing energy or variance alone. We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling, which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.     

随机矩阵的本征值外推性质

外推近似方法在原子核壳模型上取得了一些成功,然而人们对于其原理知道得比较少。这里主要研究并讨论了随机两体系综和高斯正交系综最小本征值。利用截断空间的外推解释了高斯正交系综下的外推公式以及随机两体系综下本征值外推收敛的鲁棒性,即对于壳模型有效相互作用而言,用外推法预言最低本征值收敛性很好。Although the extrapolation method of diagonalizing the nuclear shell model Hamiltonian is successful, its foundation has not yet been understand very well. In this paper, we study this approach by using random matrices with the focus on gaussian ensemble and two-body random ensemble. We derive the formula of the extrapolation method of diagonalizing the matrices of Gaussian orthogonal ensemble, and discuss the robustness of the extrapolation property by two-body random ensemble. We point out that the extrapolation method of diagonalizing the shell model Hamiltonian works better with the realistic interaction than other interactions.     

图像复原算法的频谱恢复特性分析研究

基于高斯函数假设的频谱分析方法,对逆滤波法、约束最小平方滤波法和最大似然法等三种图像复原算法的频谱恢复特性进行了实验和分析。假设光学传递函数H和图像频谱函数G为高斯函数,利用方差和方差比作为频谱宽度的分析评价指标,这是一种新的基于图像复原方法的频谱恢复特性分析法。在实验分析中,对H和G曲线设定两组方差,分为无噪声和有噪声两种情况,计算出各种算法的频谱曲线■及其方差和方差比。对由曲线图和数据给出的定性和定量结论进行了分析。