Expectation Values Of Physical Quantities Research Articles

Systematic study of the relationship between nuclear structure and reactions for the 10Be nucleus

Abstract We systematically investigate the relationship between the nuclear structure and reaction in the 10Be nucleus using a theoretical framework. The structure of the 10Be nucleus is constructed with a cluster model based on a microscopic viewpoint. In this paper, the 10Be nucleus is prepared with different structures by manipulating the parameters of an effective nucleon–nucleon interaction. The nuclear structure and expectation values of physical quantities are drastically changed by the modification. We summarize such changes and show the effects on the elastic and inelastic scatterings for proton and 12C targets in the microscopic coupled-channel calculation. Of especial interest, we recently reported the visualization of the dineutron correlation in 10Be on proton inelastic scattering in [Phys. Rev. C 104, 034613 (2021)]. In this preceding work, we found that changing the degree of dineutron correlation in 10Be leads to drastic changes of the inelastic cross section for the 2$_2^+$ state. The development (or breaking) of the dineutron correlation is governed by the strength of the spin–orbit interaction of the structure calculation. However, in the previous work, some of the realistic physical points were missing, for example, the binding energy (BE). Therefore, we reconstruct the 10Be nucleus by adjusting the effective nucleon–nucleon interaction to obtain a reasonable BE of the ground state. With this improvement, we again discuss the dineutron correlation in the 10Be nucleus. We reconfirm the way to measure the degree of development (or breaking) of the dineutron cluster structure: its sensitivity to the inelastic cross section of the 2$_2^+$ state of 10Be. Subject Index cluster model, folding model, dineutron correlation, effective nucleon-nucleon interaction.

A random-sampling method as an efficient alternative to variational Monte Carlo for solving Gutzwiller wavefunctions

We present a random-sampling (RS) method for evaluating expectation values of physical quantities using the variational approach. We demonstrate that the RS method is computationally more efficient than the variational Monte Carlo method using the Gutzwiller wavefunctions applied on single-band Hubbard models as an example. Non-local constraints can also been easily implemented in the current scheme that capture the essential physics in the limit of strong on-site repulsion. In addition, we extend the RS method to study the antiferromagnetic states with multiple variational parameters for 1D and 2D Hubbard models.

Renormalization group theory of molecular dynamics

Large scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of 2^{n(D+1)} over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as nu =0.63pm 0.01. In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number Dell 1.

LIMAO: Cross-platform software for simulating laser-induced alignment and orientation dynamics of linear-, symmetric- and asymmetric tops

A user-friendly and cross-platform software called Laser-Induced Molecular Alignment and Orientation simulator (LIMAO) has been developed. The program can be used to simulate within the rigid rotor approximation the rotational dynamics of gas phase molecules induced by linearly polarized intense laser fields at a given temperature. The software is implemented in the Java and Mathematica programming languages. The primary aim of LIMAO is to aid experimental scientists in predicting and analyzing experimental data representing laser-induced spatial alignment and orientation of molecules. Program summaryProgram title: LIMAOProgram Files doi: http://dx.doi.org/10.17632/x7h287gc9p.1Licensing provisions: GNU General Public License 3 (GPL)Programming languages: JAVA, MathematicaSupplementary material: LIMAO_SM.pdfNature of problem: LIMAO is a user-friendly software, which can be used to compute the temporal evolution of the laser-induced alignment and orientation [1-3] of gas phase molecules at a given temperature within the rigid rotor approximation. The user is asked to provide (i) molecular parameters such as rotational constant(s), a dipole moment, polarizabilities, and nuclear spin-statistical weights for the rotational levels, (ii) external field parameters such as time when the laser pulse becomes maximum, the pulse width, the intensity and carrier frequency of laser pulse(s), and (iii) temperature as input data. As an output, LIMAO generates the temporal evolution of the expectation values of physical quantities of molecules representing the spatial alignment and orientation.Solution method: LIMAO solves numerically the time-dependent Schrödinger equation of a rigid rotor molecule interacting with a time-dependent external field. The time-dependent rotational wave packet is expanded by the field-free stationary rotational eigenstates of the system. The solution is obtained by the following four steps: (i) the rotational eigenstates are derived and their symmetries within the corresponding molecular rotation group are assigned, (ii) the matrix representation of the time-dependent Hamiltonian, containing the interaction terms with an external light field as well as the matrix representations of physical quantities to be observed are constructed using the rotational eigenstates, (iii) the initial populations in the respective rotational eigenstates are determined by the Boltzmann distribution at a given temperature, and (iv) the wave packets are propagated in time and the expectation values of the relevant physical quantities are computed as a function of time.Additional comments including Restrictions and Unusual features: Simulations with the LIMAO software are limited to the rotational degrees of freedom. Light-induced vibrational excitations are neglected and light-induced electronic excitations are only accounted for in a perturbative manner through molecular polarizabilities. Therefore, the results obtained by LIMAO simulations should be treated with caution when dynamical processes such as light-induced deformation of geometrical structure, resonant vibrational excitation, and electronic excitation beyond the perturbative regime need to be considered.

HOW TO CONSTRUCT THE PROPER GAUGE-INVARIANT DENSITY MATRIX IN STEADY-STATE NONEQUILIBRIUM: APPLICATIONS TO SPIN-TRANSFER AND SPIN-ORBIT TORQUES

Experiments observing spin density and spin currents (responsible for, e.g., spin-transfer torque) in spintronic devices measure only the nonequilibrium contributions to these quantities, typically driven by injecting unpolarized charge current or by applying external time-dependent fields. On the other hand, theoretical approaches to calculate these quantities operate with both the nonequilibrium (carried by electrons around the Fermi surface) and the equilibrium (carried by the Fermi sea electrons) contributions to them. Thus, an unambiguous procedure should remove the equilibrium contributions, thereby rendering the nonequilibrium ones which are measurable and satisfy the gauge-invariant condition according to which expectation values of physical quantities should not change when electric potential everywhere is shifted by a constant amount. Using the framework of nonequilibrium Green functions, we delineate such procedure which yields the proper gauge-invariant nonequilibrium density matrix in the linear-response and elastic transport regime for current-carrying steady state of an open quantum system connected to two macroscopic reservoirs. Its usage is illustrated by computing: (i) conventional spin-transfer torque (STT) in asymmetric F/I/F magnetic tunnel junctions (MTJs); (ii) unconventional STT in asymmetric N/I/F semi-MTJs with the strong Rashba spin–orbit coupling (SOC) at the I/F interface and injected current perpendicular to that plane; and (iii) current-driven spin density within a clean ferromagnetic Rashba spin-split two-dimensional electron gas (2DEG) which generates SO torque in laterally patterned N/F/I heterostructures when such 2DEG is located at the N/F interface and injected charge current flows parallel to the plane. We also compare our results for these three examples with those that would be obtained using improper expressions for the density matrix, which are often found in the literature but which arbitrarily mix nonequilibrium and equilibrium expectation values due to a violation of the gauge invariance.

The Generalized Thermo Jaynes–Cummings Model and Its Energy Spectrum

By analyzing the characteristics of thermo field dynamics, we present a new generalized thermo Jaynes-Cummings (TJC) model at finite temperature including the thermal effects and expatiate on its physical explanation. By virtue of Lewis-Riesenfeld invariant method, we obtain its exact eigenenergy spectrum and the explicit expressions for the evolution operator of the wavefunctions. In addition, we evaluate various expectation values of physical quantities and find the pseudo-invariant eigen-operator for the generalized TJC Hamiltonian.

Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator

A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved. The solution yields the spectral resolution of the Liouvillian, that is, all eigenvalues and eigenprojections are obtained. This spectral resolution is discussed in depth in the context of the biorthogonal system and the rigged Hilbert space, and the contribution of each eigenprojection to expectation values of physical quantities is revealed. We also construct the ladder operators of the Liouvillian, which clarify the structure of the spectral resolution.

A study of the Colle-Salvetti functional for ρ2 via an exactly soluble problem

The Colle-Salvetti functional for correlation energy has given remarkably good results. It is based on approximating the second order density matrix with a particularly judicious form and using the constraining equation between the first order and second order reduced density matrices. We have used an exactly soluble N-body problem to study some aspects of the functional approximation. This has been done by calculating the reduced density matrices exactly and comparing them to the approximate form proposed by Colle and Salvetti and by comparing the expectation values of physical quantities using the approximate and exact density matrices.

Alternative sampling for variational quantum Monte Carlo

Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within many-body quantum mechanics, and these multidimensional integrals may be estimated using Monte Carlo methods. In a previous publication it has been shown that for the simplest, most commonly applied strategy in continuum quantum Monte Carlo, the random error in the resulting estimates is not well controlled. At best the central limit theorem is valid in its weakest form, and at worst it is invalid and replaced by an alternative generalized central limit theorem and non-normal random error. In both cases the random error is not controlled. Here we consider a new "residual sampling strategy" that reintroduces the central limit theorem in its strongest form, and provides full control of the random error in estimates. Estimates of the total energy and the variance of the local energy within variational Monte Carlo are considered in detail, and the approach presented may be generalized to expectation values of other operators, and to other variants of the quantum Monte Carlo method.

Geometry of escort distributions.

Given an original distribution, its statistical and probabilistic attributes may be scanned using the associated escort distribution introduced by Beck and Schlögl and employed in the formulation of nonextensive statistical mechanics. Here, the geometric structure of the one-parameter family of the escort distributions is studied based on the Kullback-Leibler divergence and the relevant Fisher metric. It is shown that the Fisher metric is given in terms of the generalized bit variance, which measures fluctuations of the crowding index of a multifractal. The Cramér-Rao inequality leads to a fundamental limit for the precision of the statistical estimate of the order of the escort distribution. We also show quantitatively that it is inappropriate to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics.

Classical Limit of Expectation Values in a Wave Packet Involving Few Stationary States

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejer's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejer's average. The quantum uncertainty is then demonstrated to have a classical counterpart.

Mittag-Leffler coherent states

We create a family of boson coherent states using the functions of Mittag-Leffler (ML) E(z), (>0) and their generalizations E,(z), (,>0) instead of exponentials. These states are shown to satisfy the usual requirements of normalizability, continuity in the label and the resolution of unity with a positive weight function. This last quantity is found for arbitrary ,>0 as a solution of an associated Stieltjes moment problem. In addition, for = m = 1,2,3 ... and = 1 (corresponding to Em(z)) we propose and analyse special q-deformations (0<q1) of the functions Em(z) which serve as a tool to define q-deformed coherent states of ML type. We provide the expressions for expectation values of physical quantities for all the above states. We discuss physical properties of these states, noting that they are squeezed. The ML coherent states are sub-Poissonian in nature, whereas the q-deformed ML states can be sub- and super-Poissonian depending on q. All these states are shown to be eigenstates of deformed boson operators whose commutation relations are given.

High-Temperature Dynamics of Spin Glasses

We develop a systematic expansion method of physical quantities for the SK model and the finite-dimensional $\pm J$ model of spin glasses in non-equilibrium states. The dynamical probability distribution function is derived from the master equation using a high temperature expansion. We calculate the expectation values of physical quantities from the dynamical probability distribution function. The theoretical curves show satisfactory agreement with Monte Carlo simulation results in the appropriate temperature and time regions. A comparison is made with the results of a dynamics theory by Coolen, Laughton and Sherrington.

New Formulation of One-body Problem in Quantum Electrodynamics

One electron states at time t are reasonably defined and the space spanned by them is denoted by .pI (t). One electron problem is clearly formulated using .pIe. The motion of the projection of a given state 1jI' onto .pI' is described by the wave function. If 1jI'is in -Pr6(-oo) the wave function satisfies the equation given by Schwinge.·. Theptobability of staying in one-electron s~ate and the expectation values of physical quantities are written as the generalized form of ordinary quantum mechanics so as to indicate the non·local character of our theory. The expectation value of energy has the imaginary part concerned with the damping property. The application to the problem of lamb shift and line breadth is made for example. Divergence difficulties are not concerned.