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We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems. [ABSTRACT FROM AUTHOR]

In this paper, we study two quasi-one-dimensional (1D) Kitaev models with ladder-like and tube-like spatial structures, respectively. Our results provide the phase diagrams and explicit expressions of the Majorana zero modes. The topological phase diagrams are obtained by decomposing the topological invariants and the topological conditions for topologically nontrivial phases are given precisely. For systems which belongs to topological class BDI, we obtain the regions in the phase diagrams where the topological numbers show even-odd effect. For the Kitaev tube model a phase factor induced by the magnetic flux in the axial direction of the tube is introduced to alter the classification of the tube Hamiltonian from class BDI to D. The Kitaev tube of class D is characterized by the index when the number of chains is odd while 0, 1, 2 when the number of chains is even. The phase diagrams show periodic behaviors with respect to the magnetic flux. The bulk-boundary correspondence is demonstrated by the observations that the topological conditions for the bulk topological invariant to take nontrivial values are precisely those for the existence of the Majorana zero modes. [ABSTRACT FROM AUTHOR]

The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamilton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equations are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]

We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level system, we derive the transitionless driving Hamiltonian for the local adiabatic quantum search algorithm. We found that when adding a transitionless quantum driving term HD(t) on the local adiabatic quantum search algorithm, the success rate is 1 exactly with arbitrary evolution time by solving the time-dependent Schr¨odinger equation in eigen-picture. Moreover, we show the reason for the drastic decrease of the evolution time is that the driving Hamiltonian increases the lowest eigenvalues to a maximum of . [ABSTRACT FROM AUTHOR]

The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied. For a specific regime of the parameters (tx = tp, ty < 0), the exact ground-state is found analytically, which is a dimerized insulator with one electron bound in each rung of the ladder. For the case tx,ty,tp > 0, the system is exactly studied using quantum Monte Carlo (QMC) method without a sign problem. It is found that the system is a Mott insulator for small tp and a quantum phase transition to a superfluid phase is driven by increasing tp. The critical is determined precisely by a scaling analysis. Since it is possible that the Creutz ladder is realized experimentally, the theoretical results are interesting to the cold-atom experiments. [ABSTRACT FROM AUTHOR]

We have deduced analytical solutions of an energy level diagram of the doubly driven/dressed atom for a two-level atom exposed to a strong near-resonant bichromatic laser field in a special case, i.e., the bichromatic field with frequencies ω1 and ω2, and Rabi frequencies and , in which the first coupling field of acts on the bare atomic levels, and then the resulting singly dressed states are driven by the second coupling field of , thus resulting in the doubly dressed atom. We have measured the probe absorption spectra of a doubly driven two-level atom. The system consists of 5 and 5 states of 87Rb atoms in a magneto-optical trap (MOT) as well as the cooling/trapping beams and an additional coupling field. As for the spectroscopic properties of the doubly driven two-level atom, theoretical analytical solutions are in general agreement with the experimental spectrum as a whole. [ABSTRACT FROM AUTHOR]

We use the Bethe ansatz method to investigate the Schrödinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl(2) hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl(2) Lie algebra. It is found that the results of the two methods are the same. [ABSTRACT FROM AUTHOR]

In quantum metrology we usually extract information from the reduced probe system but ignore the information lost inevitably into the environment. However, K. Mølmer [Phys. Rev. Lett.114, 040401 (2015)] showed that the information lost into the environment has an important effect on improving the successful probability of quantum process discrimination. Here we reconsider the model of a driven atom coupled to an environment and distinguish which of two candidate Hamiltonians governs the dynamics of the whole system. We mainly discuss two measurement methods, one of which obtains only the information from the reduced atom state and the other obtains the information from both the atom and its environment. Interestingly, for the two methods the optimal initial states of the atom, used to improve the successful probability of the process discrimination, are different. By comparing the two methods we find that the partial information from the environment is very useful for the discriminations. [ABSTRACT FROM AUTHOR]

The phonon-assisted process of energy transfer aiming at exploring the newly emerging frontier between biology and physics is an issue of central interest. This article shows the important role of the intramolecular vibrational modes for excitation energy transfer in the photosynthetic systems. Based on a dimer system consisting of a donor and an acceptor modeled by two two-level systems, in which one of them is coupled to a high-energy vibrational mode, we derive an effective Hamiltonian describing the vibration-assisted coherent energy transfer process in the polaron frame. The effective Hamiltonian reveals in the case that the vibrational mode dynamically matches the energy detuning between the donor and the acceptor, the original detuned energy transfer becomes resonant energy transfer. In addition, the population dynamics and coherence dynamics of the dimer system with and without vibration-assistance are investigated numerically. It is found that, the energy transfer efficiency and the transfer time depend heavily on the interaction strength of the donor and the high-energy vibrational mode, as well as the vibrational frequency. The numerical results also indicate that the initial state and dissipation rate of the vibrational mode have little influence on the dynamics of the dimer system. Results obtained in this article are not only helpful to understand the natural photosynthesis, but also offer an optimal design principle for artificial photosynthesis. [ABSTRACT FROM AUTHOR]

The effect of tensile uniaxial strain on the non-parabolic electronic band structure of armchair graphene nanoribbon (AGNR) is investigated. In addition, the density of states and the carrier statistic based on the tight-binding Hamiltonian are modeled analytically. It is found that the property of AGNR in the non-parabolic band region is varied by the strain. The tunable energy band gap in AGNR upon strain at the minimum energy is described for each of n-AGNR families in the non-parabolic approximation. The behavior of AGNR in the presence of strain is attributed to the breakable AGNR electronic band structure, which varies the physical properties from its normality. The linear relation between the energy gap and the electrical properties is featured to further explain the characteristic of the deformed AGNR upon strain. [ABSTRACT FROM AUTHOR]

We present the behaviors of both dynamical and static charge susceptibilities of undoped armchair graphene nanoribbon using the Green’s function approach in the context of tight binding model Hamiltonian. Specifically, the effects of magnetic field on the the plasmon modes of armchair graphene nanoribbon are investigated via calculating the correlation function of charge density operators. Our results show that the increase of magnetic field makes the high-frequency plasmon mode for both metallic and insulating cases disappear. We also show that low-frequency plasmon mode for metallic nanoribbon appears due to increase of magnetic field. Furthermore, the number of collective excitation modes increases with ribbon width at zero magnetic field. Finally, the temperature dependence of the static charge structure factor of armchair graphene nanoribbon is studied. The effects of both magnetic field and ribbon width on the static charge structure factor are discussed in detail. [ABSTRACT FROM AUTHOR]

Multi-mode cavities have now attracted much attention both experimentally and theoretically. In this paper, inspired by recent experiments of cavity-assisted Raman transitions, we realize a two-axis spin Hamiltonian in two cavities. This realized Hamiltonian has a distinct property that all parameters can be tuned independently. For proper parameters, the well-studied one- and two-axis twisting Hamiltonians are recovered, and the scaling of N−1 of the maximal squeezing factor can occur naturally. On the other hand, in the two-axis twisting Hamiltonian, spin squeezing is usually reduced when increasing the atomic resonant frequency ω0. Surprisingly, we find that by combining with the dimensionless parameter χ (> −1), this atomic resonant frequency ω0 can enhance spin squeezing greatly. These results are beneficial for achieving the required spin squeezing in experiments. [ABSTRACT FROM AUTHOR]

In this paper, we present the fractional Hamilton’s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton’s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. [ABSTRACT FROM AUTHOR]

A quantum chain model of multiple molecule motors is proposed as a mathematical physics theory for the microscopic modeling of classical force-velocity relation and tension transients in muscle fibers. The proposed model was a quantum many-particle Hamiltonian to predict the force-velocity relation for the slow release of muscle fibers, which has not yet been empirically defined and was much more complicated than the hyperbolic relationships. Using the same Hamiltonian model, a mathematical force-velocity relationship was proposed to explain the tension observed when the muscle was stimulated with an alternative electric current. The discrepancy between input electric frequency and the muscle oscillation frequency could be explained physically by the Doppler effect in this quantum chain model. Further more, quantum physics phenomena were applied to explore the tension time course of cardiac muscle and insect flight muscle. Most of the experimental tension transient curves were found to correspond to the theoretical output of quantum two- and three-level models. Mathematical modeling electric stimulus as photons exciting a quantum three-level particle reproduced most of the tension transient curves of water bug Lethocerus maximus. [ABSTRACT FROM AUTHOR]

For lower dimensional Fermi–Pasta–Ulam (FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the Hénon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α(t) and β(t) with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. [ABSTRACT FROM AUTHOR]

In this paper, the ascent of 2× 2 infinite dimensional Hamiltonian operators and a class of 4× 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2× 2 infinite dimensional Hamiltonian operator is 1 and the ascent of a class of 4× 4 infinite dimensional Hamiltonian operators that arises in study of elasticity is 2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions. [ABSTRACT FROM AUTHOR]

In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results. [ABSTRACT FROM AUTHOR]

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by El-Nabulsi. First, the El-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and El-Nabulsi—Hamilton's canonical equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of El-Nabulsi—Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of El-Nabulsi—Hamilton action under the infinitesimal transformations of the group. Finally, Noether's theorems for the non-conservative Hamilton system under the El-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system. [ABSTRACT FROM AUTHOR]

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed, the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]