Coherent State Method Research Articles

Coupled coherent states method for tunneling dynamics: an interpretative study

Coupled coherent states method for tunneling dynamics: an interpretative study

Assessing the Accuracy of Quantum Dynamics Performed in the Time-Dependent Basis Representation.

A full quantum-mechanical (QM) description of large amplitude nuclear motion, associated with chemical reactions or isomerization of high-dimensional molecular systems, is inherently challenging due to the exponential scaling of the QM complexity with system size. To ameliorate the scaling bottleneck in studies of realistic systems, typically modeled in the configuration space, the nuclear wave functions are represented in terms of time-dependent basis functions. Such bases are expected to give an accurate description with a modest number of basis functions employed, by adapting them to the wave function solving the time-dependent Schrödinger equation. It is not, however, straightforward to estimate the accuracy of the resulting solution: in QM the energy conservation, a convenient such measure for a classical trajectory evolving in a time-independent potential, is not a sufficient criterion of the dynamics' accuracy. In this work, we argue that the expectation value of the Hamiltonian's "variance", quantifying the basis completeness, is a suitable practical measure of the quantum dynamics' accuracy. Illustrations are given for several chemistry-relevant test systems, modeled employing time-independent as well as time-dependent bases, including the coupled and variational coherent states methods and the quantum-trajectory guided adaptable Gaussians (QTAG) as the latter basis type. A novel semilocal definition of the QTAG basis time-evolution for placing the basis functions "in the right place at the right time" is also presented.

The Sound Field Intensity Distribution in the Deep Sea in the “Depth—Angle–Time” Phase Space

The transition from the traditional representation of the wave field in the vertical section of an underwater sound channel as a function of depth and time to the distribution of this field in the 3D phase space “depth–angle–time” is considered. For this purpose, the method of coherent states developed in quantum theory is used. The meaning of the proposed transition is that the field intensity distribution in the specified phase space is less sensitive to sound velocity fluctuations than in the original 2D depth–time space. This fact can be used in solving inverse problems. As an example, we consider the reconstruction of the coordinates of a source in a waveguide from measurements of the field intensity distribution of this source in phase space.

Nonparaxial Focusing of Partially Coherent Gaussian Schell-Model and Bessel-Correlated Beams in Free Space

The nonparaxial focusing of partially coherent beams in free space has been studied using the coherent-state and coherent-mode decomposition methods. Analytical expressions for the width and angular divergence of partially coherent Gaussian Schell-model (GSM) beams have been obtained using the coherent-state method. It has been shown that the focusing plane is shifted in the opposite axial direction compared to the geometric focusing plane. The influence of the nonparaxiality and spatial coherence of Bessel-correlated vortex beams on the intensity distribution and displacement of the focus plane has been analyzed. It has been shown that the shift of the focus plane increases with a decrease in the coherence radius of the source. A smaller diffraction spread has been shown for partially coherent Bessel-correlated beams compared to GSM beams.

COMPREHENSIVE DESIGN-ORIENTED MODEL FOR FRP-CONFINED CIRCULAR RC COLUMNS

Today, the use of fiber-reinforced polymers (FRPs) for the confinement of reinforced concrete (RC) columns is a state-of-the-art technic in the strengthening of existing structures. Thus far, various design models are present in literature to predict the stress-strain behavior and to allow for the ultimate limit state design of FRP-confined concrete. Often, the models proposed are scientific in nature only, they are just designed for plain concrete specimens, and they do not meet the demands necessary for practical use. Therefore, this paper presents a comprehensive design-oriented model for FRP-confined circular RC columns considering both the ultimate limit state (ULS) and the serviceability limit state (SLS). Beside equations to calculate the new ultimate confined concrete strength and the accompanying axial strain, the paper introduces an approach to generate a stress block simplifying the design procedure for columns subjected to combined compression and bending. Furthermore, an equation is presented to allow for the calculation of a combined partial safety factor taking into account the material safety factors of both the concrete of the column and the FRP system used. In order to realize a proper and coherent limit state method, the entire model uses characteristic material values and equations only. At last, the SLS is addressed with a simple approach limiting the maximal concrete compressive stress.

COMPREHENSIVE DESIGN-ORIENTED MODEL FOR FRP-CONFINED CIRCULAR RC COLUMNS

Today, the use of fiber-reinforced polymers (FRPs) for the confinement of reinforced concrete (RC) columns is a state-of-the-art technic in the strengthening of existing structures. Thus far, various design models are present in literature to predict the stress-strain behavior and to allow for the ultimate limit state design of FRP-confined concrete. Often, the models proposed are scientific in nature only, they are just designed for plain concrete specimens, and they do not meet the demands necessary for practical use. Therefore, this paper presents a comprehensive design-oriented model for FRP-confined circular RC columns considering both the ultimate limit state (ULS) and the serviceability limit state (SLS). Beside equations to calculate the new ultimate confined concrete strength and the accompanying axial strain, the paper introduces an approach to generate a stress block simplifying the design procedure for columns subjected to combined compression and bending. Furthermore, an equation is presented to allow for the calculation of a combined partial safety factor taking into account the material safety factors of both the concrete of the column and the FRP system used. In order to realize a proper and coherent limit state method, the entire model uses characteristic material values and equations only. At last, the SLS is addressed with a simple approach limiting the maximal concrete compressive stress.

Effect of impurity on modulational instability of localized modes in a discrete quantum ferromagnetic spin chain

The modulational instability (MI) of localized modes in a discrete quantum ferromagnetic spin chain with the effect of impurity is studied in this paper. The model of Heisenberg ferromagnetic spin chain is considered and dynamical equation is derived by the use of Glauber’s coherent state method along with Holstein-Primakoff (H-P) bosonic representation of spin operators. The dynamical equation is in the form of discrete nonlinear Schro¨dinger (DNLS) equation which describes the complete dynamics of ferromagnetic spin chain. The MI technique is applied to the DNLS equation and obtains the dispersion relation which relates the frequency and wavenumber of the modulating perturbations. Using dispersion relation, we establish the stability criteria of the spin waves in ferromagnetic spin chain and explore how the presence of impurity supports the formation of localized modes as shown in the stability/instability profile. With the use of graphical illustrations of MI, the strength of impurity on the stability/instability of localized modes in ferromagnetic spin chain is discussed. Through numerical simulation, we explore how the role of impurity supports the excitation of localized modes in ferromagnetic chain and also analyze the short time and long time evolution of localized wave in ferromagnetic spin chain.

High-order harmonic generation by static coherent states method in single-electron atomic and molecular systems.

We solve the time-dependent Schrodinger equation using the coherent states as basis sets for computing high harmonic generation (HHG) in a full-dimensional single-electron "realistic" system. We apply the static coherent states (SCS) method to investigate HHG in the hydrogen molecular ion induced by a linearly polarized laser field. We show that SCS gives reasonable agreement compared to the three dimensional unitary split-operator approach. Next, we study isolated attosecond pulse generation in . To do so, we employ the well-known polarization gating technique, which combines two delayed counter-rotating circular laser pulses, and opens up a gate at the central portion of the superposed pulse. Our results suggest that the SCS method can be used for full-dimensional quantum simulation of higher dimensional systems such as the hydrogen molecule in the presence of an external laser field.

Reduced Density Matrix and Quantum Correlation in Two-Qubit Quantum Rabi Model

In this work, we give an analytical derivation of the reduced density matrix between two qubits in a cavity field, which is described by the quantum Rabi model. Using the coherent state method and the generalized hypergeometric functions, we find a complete solution of the 4-by-4 reduced density matrix for each eigen energy by taking the partial trace over the cavity field states. Four kinds of measurements used to describe the quantum entanglement and quantum correlation between the two qubits, i.e., the concurrence, quantum discord, steerable weight, and robustness of coherence, are calculated for the ground state and excited states. For both the weak coupling ( $g\rightarrow 0$ ) and deep-strong coupling ( $g\rightarrow \infty $ ) regimes, quantum entanglement and quantum correlation between the two qubits are vanishing. An appropriate coupling in the deep strong coupling regime between the qubits and the cavity field is required if one wants to establish quantum entanglement between the qubits.

Generalized coherent-squeezed-state expansion for the super-radiant phase transition

We develop a systematic variational coherent-squeezed-state expansion for the ground state of the quantum Rabi model, which includes an additional squeezing effect with comparisons to previous coherent-state approach. For finite large ratio between the atomic and field frequency, the essential feature of the ground-state wave function in the super-radiant phase appears, which has a structure of two delocalized wake packets. The single-peaked wave function with one coherent-squeezed state works well even around the critical regime, exhibiting the advantage over the coherent-state method. As the coupling increases to form strong correlations physics in the vicinity of phase transition, we develop an improved wave function with a structure of two Gaussian wave packets, which is a linear superposition of two coherent-squeezed state. The ground-state energy and the average photon number agree well with numerical ones even in the strong-correlated regimes, exhibiting a substantial improvement over the coherent-state expansion. The advantage of the coherent-squeezed-state expansion lies in the inclusion of the second coherent-squeezed state and the additional squeezed deformation of the wave function, providing a useful tool for multi-modes spin-boson coupling systems of greater complexity.

Matrix geometry for ellipsoids

Abstract We study description of ellipsoids by matrices to gain insights into emergence of space in matrix models. We apply the coherent state method to the fuzzy ellipsoids and perform the Berezin-Toeplitz quantization for ellipsoids. We see that the manifold described by the coherent state method is an ellipsoid. We find that the Toeplitz operators obtained in the Berezin-Toeplitz quantization agree with the matrices for the fuzzy ellipsoids used in the coherent state method and that the wave functions in the above two methods coincide.

Triaxial nuclear shapes of even–even ruthenium isotopic chain in the O(6) dynamical symmetry of interacting boson model with the three-body quadrupole interaction

Even–even nuclei in the $$ A\sim100 $$ mass region are investigated within the framework of the sd-interacting boson model (sdIBM1) with three-body O(6) symmetric quadrupole operator $$ \left[ {QQQ} \right]^{\left( 0 \right)} $$ for generating states with triaxial deformation. The rigid triaxial asymmetric rotor model of collective rotation is used to extract the asymmetry parameter $$ \gamma $$ from both the energy ratio of the second $$ 2_{2}^{ + } $$ state to the first $$ 2_{1}^{ + } $$ state and the reduced E2 transition probabilities from $$ 2_{1,2}^{ + } $$ states to the ground state. Using the method of the intrinsic coherent states, the classical limit of potential energy surfaces which represents the expectation value of the total Hamiltonian is obtained. The critical points of the phase transition are investigated. The triaxiality is analyzed for even–even ruthenium (Ru) isotopic chain as an example of illustrating the effect of the three-body quadrupole operator. By using computer simulated search program, a fitting procedure is performed to get the best parameters of the IBM Hamiltonian for each nucleus in order to obtain a minimum root mean square deviation between the calculated and the experimental some low-lying energy levels and B(E2) transition rates.

Quantum system-bath dynamics with quantum superposition sampling and coupled generalized coherent states

Previously, we introduced two versions of the Multiconfigurational Ehrenfest (MCE) approach to high dimensional quantum dynamics. It has been shown that the first version, MCEv1, converges well to the existing benchmarks for high dimensional model systems. At the same time, it was found that the second version, MCEv2, had more difficulty converging in some regimes. As MCEv2 is particularly suited for direct dynamics, it is important to facilitate its convergence. This paper investigates an efficient method of basis set sampling, called Quantum Superposition Sampling (QSS), which dramatically improves the performance of the MCEv2 approach. QSS is tested on the spin-boson model, often used for modeling of open quantum systems. It is also shown that the quantum subsystem in the spin-boson model can be conveniently treated with the help of two level system coherent states. Generalized coherent states, which combine two level system coherent states for the description of the system and Gaussian coherent states for description of the bath, are introduced. Various forms of quantum equations of motion in the basis of generalized coherent states can be developed by analogy with known quantum dynamics equations in the basis of Gaussian coherent states; in particular, the multiconfigurational Ehrenfest method becomes a version of coupled generalized coherent states, and QSS can then be viewed as a generalization of a sampling method known for the existing coupled coherent states method which uses Gaussian coherent states.

Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

In this report, we introduce the static coherent states (SCS) method for investigating quantum electron dynamics in a one- or two-electron laser-induced system. The SCS method solves the time-dependent Schrödinger equation (TDSE) both in imaginary and real times on the basis of a static grid of coherent states (CSs). Moreover, we consider classical dynamics for the nuclei by solving their Newtonian equations of motion. By implementing classical nuclear dynamics, we compute the electronic-state potential energy curves of H2+ in the absence and presence of an ultra-short intense laser field. We used this method to investigate charge migration in H2+. In particular, we found that the charge migration time increased exponentially with inter-nuclear distance. We also observed substantial charge localization for sufficiently long molecular bonds.

Commutative geometry for non-commutative D-branes by tachyon condensation

There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-abelian. We show that we can use tachyon condensation to determine the position or the shape of D0-branes uniquely as a commutative region in spacetime together with non-trivial gauge flux on it, even if the scalar fields are non-abelian. We use the idea of the so-called coherent state method developed in the field of matrix models in the context of the tachyon condensation. We investigate configurations of noncommutative D2-brane made out of D0-branes as examples. In particular, we examine a Moyal plane and a fuzzy sphere in detail, and show that whose shapes are commutative $\mathbb{R}^2$ and $S^2$, respectively, equipped with uniform magnetic flux on them. We study the physical meaning of this commutative geometry made out of matrices, and propose an interpretation in terms of K-homology.

Complementary version of fermion coupled coherent states method and gram-schmidt algorithm: Theory and applications for electronic states of H2 and H2.

In our previous report, we introduced a new version of Fermion coupled coherent states method (FCCS) which was especially suited for simulating the first symmetric spatial electronic state of two-electron systems. In this manuscript, we report a complementary version for FCCS method to simulate both of the first symmetric and antisymmetric spatial electronic states of two-electron systems. Moreover, the Gram-Schmidt orthogonalization process is employed to reach the excited states of the system. We apply this FCCS method and the original coupled coherent state method to simulate the energy of different electronic states of H2 and H2+, respectively. The results for the energy of computed electronic states of H2 and H2+ show a pretty good consistency with the exact values. © 2017 Wiley Periodicals, Inc.

Quantum Coherent States and Path Integral Method to Stochastically Determine the Anisotropic Volume Expansion in Lithiated Silicon Nanowires

This computational research study will analyze the multi-physics of lithium ion insertion into a silicon nanowire in an attempt to explain the electrochemical kinetics at the nanoscale and quantum level. The electron coherent states and a quantum field version of photon density waves will be the joining theories that will explain the electron-photon interaction within the lithium-silicon lattice structure. These two quantum particles will be responsible for the photon absorption rate of silicon atoms that are hypothesized to be the leading cause of breaking diatomic silicon covalent bonds that ultimately leads to volume expansion. It will be demonstrated through the combination of Maxwell stress tensor, optical amplification and path integrals that a stochastic analyze using a variety of Poisson distributions that the anisotropic expansion rates in the <110>, <111> and <112> orthogonal directions confirms the findings ascertained in previous works made by other research groups. The computational findings presented in this work are similar to those which were discovered experimentally using transmission electron microscopy (TEM) and simulation models that used density functional theory (DFT) and molecular dynamics (MD). The refractive index and electric susceptibility parameters of lithiated silicon are interwoven in the first principle theoretical equations and appears frequently throughout this research presentation, which should serve to demonstrate the importance of these parameters in the understanding of this component in lithium ion batteries.

A new version of fermion coupled coherent states method: Theory and applications in simulation of two-electron systems

We report a new version of fermion coupled coherent states method (FCCS-II) to simulate two-electron systems based on a self-symmetrized six-dimensional (6D) coherent states grid. Unlike the older fermion coupled coherent states method (FCCS-I), FCCS-II does not need any new equations in comparison with the coupled coherent states method. FCCS-II uses a simpler and more efficient approach for symmetrizing the spatial wave function in the simulation of fermionic systems. This method, has significantly increased the speed of computations and give us the capability to simulate the quantum systems with the larger CS grids. We apply FCCS-II to simulate the Helium atom and the Hydrogen molecule based on grids with a large numbers of coherent states. FCCS-II with a relatively low number of CS gives a potential energy curve for H2that is very close to the exact potential curve. Moreover, we have re-derived all the important equations of the FCCS-I method.

Multiconfigurational quantum propagation with trajectory-guided generalized coherent states.

A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.

Traces of Intertwiners for Quantum Affine $${\mathfrak{sl}}_2$$ and Felder–Varchenko Functions

We show that the traces of $U_q(\widehat{\mathfrak{sl}}_2)$-intertwiners of Etingof-Schiffmann-Varchenko valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder-Varchenko's hypergeometric solutions to the $q$-KZB heat equation. This gives the first proof that such a trace function converges and resolves the first case of the Etingof-Varchenko conjecture. As applications, we prove a symmetry property for traces of intertwiners and prove Felder-Varchenko's conjecture that their elliptic Macdonald polynomials are related to the affine Macdonald polynomials defined as traces over irreducible integrable $U_q(\widehat{\mathfrak{sl}}_2)$-modules by Etingof-Kirillov Jr. In the trigonometric and classical limits, we recover results of Etingof-Kirillov Jr. and Etingof-Varchenko. Our method relies on an interplay between the method of coherent states applied to the free field realization of the $q$-Wakimoto module of Matsuo, convergence properties given by the theta hypergeometric integrals of Felder-Varchenko, and rationality properties originating from the representation-theoretic definition of the trace function.