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To explore the thermal transport procedure driven by temperature gradient in terms of linear response theory, Luttinger et al. proposed the thermal scalar and vector potential[1,2] . In this manuscript, we try to address the microscopic origin of these phenomenological thermal potentials. Based on the temperature dependent damping force derived from quantum Boltzmann equation (QBE), we express the thermal scalar and vector potential by the distribution function in damping force, which originates from the scattering of conduction electrons. We illustrate this by the scattering of electron-phonon interaction in some systems. The temperature and temperature gradient in the local equilibrium distribution function will have effect on the thermal scalar and vector potentials, which is compatible with the previous works[1,2] . The influence from quantum correction terms in QBE are also considered, which contribute not only to the damping force, but also to the anomalous velocity in the drift term. An approximated solution for the QBE is given, the numerical results for the damping force, thermal current density as well as other physical observable are shown in figures., Comment: 4figures

Quantum spin liquid has massive many spin entanglement in the ground state, we can evaluate it by the entanglement entropy, but the latter can not be observed directly by experiment. In this manuscript, we try to characterize its topological properties by the geometric phase. However the usual adiabatic or non-adiabatic geometric phase can not appear in the density matrix of entanglement entropy, so we extend it to the sub-geometric phase which can exist in the density matrix and have influence on the entanglement entropy, spin correlation function as well as other physical observable. We will demonstrate that the imaginary part of sub-geometric phase will deviate the resonance peak by an amount concerning with this phase and affect the energy level crossing, while the real part of sub-geometric phase will determine the stability of initial state, it may provide a complement on the selection rule of quantum transition., Comment: 19pages

Based on the adiabatic geometric phase concerning with density matrix[1] , we extend it to the sub-geometric phase in the non-adiabatic case. It is found that whatever the real part or imaginary part of the sub-geometric phase can play an important role in quantum transition. The imaginary part of sub-geometric phase can deviate the resonance peak in the quantum transition, which may bring modification on the level crossing, while the real part of sub-geometric phase will determine the stability of initial state according to the linear stability analysis theory, which can be regarded as somewhat complement on the selection rule of quantum transition. Finally, we illustrate them by two examples: one is the system with time-dependent perturbation, the other is a two-level system. It indicates that both the real and imaginary parts of sub-geometric phase have influence on quantum transition., Comment: 0 figures, 16pages

In this manuscript, we propose a non-equilibrium temperature by a temperature dependent Vlasov equation for the charge particles transport through a environmental reservoir. A new damping force and a inverse damping relaxation time are derived based on the Vlasov equation, which have obvious influence on the external force and the relaxation time of transport particles. The non-equilibrium temperature for the transport particles is defined by their distribution function out of equilibrium, which is different from the equilibrium temperature of reservoir. There exists heat transfer between the transport particles and the reservoir, because the whole transport particles are in non-equilibrium state. Finally, we illustrate them by an example of one-dimensional charge particles transport under an external electric field, the non-equilibrium temperature and damping force defined by us are shown numerically., Comment: 17pages,4figures

Within the spinor Boltzmann equation (SBE) formalism, we derived a temperature dependent thermal spin-orbit torque based on local equilibrium assumption in a system with Rashba spin-orbit interaction. If we expand the distribution function of spinor Boltzmann equation around local equilibrium distribution, we can obtain the spin diffusion equation from SBE, then the spin transfer torque, spin orbit torque as well as thermal spin-orbit torque we seek to can be read out from this equation. It exhibits that this thermal spin-orbit torque originates from the temperature gradient of local equilibrium distribution function, which is explicit and straightforward than previous works. Finally, we illustrate them by an example of spin-polarized transport through a ferromagnet with Rashba spin-orbit coupling, in which those torques driven whatever by temperature gradient or bias are manifested quantitatively., Comment: 15pages,6figures

Based on the principle of linearized stability proposed by Lyapounov, we investigate the robustness of Majorana zero energy state (MZES), which plays an important role in topological quantum computation. We show that the MZES is not enough robust against the external perturbations, because mathematically it is critical stable instead of the asymptotic stable, only the states with asymptotic stability can be regarded as robustness, so the MZES can not be used to carry quantum information in topological quantum computation. Our study is different from previous works that usually make the numerical test by some special perturbations, our analytical derivation is suitable for arbitrary perturbations. As an example, we demonstrate it by the stability analysis of MZES in the spin-orbit coupled semiconductor/ superconductor junction., Comment: 13 pages, 1 figures

The usual Berry phase for a Majorana zero-energy state is zero. In this manuscript, we propose a generalized geometric phase for Majorana zero-energy state, which is non-zero for the electron or hole, respectively. We calculate these non-zero geometric phases in a Ferromagnet (FI)/Topological Insulator (TI)/Superconductor (SC) hybrid system, whose magnetization can be manipulated by changing adiabatically the spin degree of freedom. The non-zero geometric phases have potential application on the topological quantum computation treatment of Majorana zero-energy modes. We also discuss the non-adiabatic geometric phase associated with Majorana zero-energy state by the path integral method., Comment: 15pages,1figure

In this letter, the generalization of geometric phase in density matrix is presented, we show that the extended sub-geometric phase have unified expression whatever in adiabatic or nonadiabatic procedure, the relations between them and the usual Berry phase or Aharonov-Anandan phase are established. We also demonstrated the influence of sub-geometric phases on the physical observables. Finally, our treatment is naturally used to investigate the geometric phase in mixed state., Comment: 10pages

The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling $J>0$ in armchair direction and ferromagnetic interaction $J'<0$ in zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio $Q_{2}$ and spin stiffness $\rho$ in two directions for various coupling ratio $\alpha=J'/J$ under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point $\alpha_c=-0.93$. Through the finite-size scaling analysis on $Q_{2}$, $\rho_{x}$ and $\rho_{y}$, we determined the critical exponent related to the correlation length $\nu$ to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing $\alpha$. A phase diagram in the coupling ratio $\alpha$-magnetic field $h$ plane is obtained, where four phases, including dimerized, stripe, canted stripe and polarized phases are identified. It is also unveiled that the temperature dependence of the specific heat $C(T)$ for different $\alpha$'s intersects precisely at one point, similar to that of liquid $^{3}$He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of $Q_{2}$, $\rho$ and $C(T)$ are carefully analyzed. The susceptibility is well compared with the experimental data to give the magnetic parameters of both compounds.

We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theory. Considering the difference of their expectation values, a generalized Bell's inequality is presented, which is coincided with the prediction of quantum mechanics., Comment: 5 pages, 0 figure

In the well known treatment of quantum teleportation, the receiver should convert the state of his EPR particle into the replica of the unknown quantum state by one of four possible unitary transformations. However, the importance of these unitary transformations must be emphasized. We will show in this paper that the receiver can not transform the state of his particle into an exact replica of the unknown state which the sender want to transfer if he have not a proper implementation of these unitary transformations. In the procedure of converting state, the inevitable coupling between EPR particle and environment which is needed by the implementation of unitary transformations will reduce the accuracy of the replica., Comment: 4 pages, 0 figure

I will replace this manuscript by a new paper, Comment: replacement