Born-Oppenheimer approximation in open systems

We generalize the standard Born-Oppenheimer approximation to the case of open quantum systems. We define the zeroth order Born-Oppenheimer approximation of an open quantum system as the regime in which its effective Hamiltonian can be diagonalized with fixed slowly changing variables. We then establish validity and invalidity conditions for this approximation for two kinds of dissipations--the spin relaxation and the dissipation of center-of-mass motion. As an example, the Born-Oppenheimer approximation of a two-level open system is analyzed.Comment: 7 pages, 3 figure

Non-Markovian Quantum Jump with Generalized Lindblad Master Equation

The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. In this paper, we extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Markovian jump approach and the computational efficiency of this method are also discussed

Are the high-Tc superconductors strongly correlated electron systems?

In this paper, we argue that the high-temperature superconductors do not belong to strong correlated electron systems. It is shown that both the two-dimensional Hubbard and t-J models are inadequate for describing high temperature superconductivity. In our opinion, a superconducting phase should be an energy minimum electronic state which can be described in a new framework where the electron-electron interactions (both on-site Hubbard term and off-site term) and the electron-phonon interaction can be completely suppressed.Comment: 4 pages, 3 figure

The Mystery of Superconductivity: Glue or No Glue?

In this study, a possible non-quasiparticle glue for superconductivity of both conventional and unconventional superconductors is explored in a pure electron picture. It is shown clearly that the moving electrons due to the electromagnetic interaction can self-organize into some quasi-one-dimensional real-space charge stripes, which can further form some thermodynamically stable vortex lattices with trigonal or tetragonal symmetry. The relationships among the charge stripes, the Cooper pairs and the Peierls phase transition are discussed. The suggested mechanism (glue) of the superconductivity may be valid for the one- and two-dimensional superconductors. We also argue that the highest critical temperature of the doped superconductors is most likely to be achieved around the Mott metal-insulator transition.Comment: 5 pages, 8 figure

A Real Space Description of the Superconducting and Pseudogap Phase

In this work, we study the relationship between the superconducting phase and pseudogap phase in a real-space picture. We suggest that the superconducting ground states are guaranteed by the energy minimum charge structure of the quasi-one-dimensional Peierls chains (static vortex lines). It is shown that there is a charge ordering phase transition from the Peierls chains (the superconducting ground state) to the periodic chains (the superconducting excited state) in any superconductors. In our scenarios, all the superconducting electrons can be considered as the "inertial electrons"at some stable zero-force positions. Furthermore, we prove analytically that two electrons, due to a short-range real space Coulomb confinement effect (the nearest-neighbor electromagnetic interactions), can be in pairing inside a single plaquette with four negative ions. This implies that the pseudogap phenomenon can be found from a wide variety of materials, not just the cuprate superconductors.Comment: 6 pages, 7 figure

Magic doping: From the localized hole-pair to the checkerboard patterns

Intensive experiments have revealed that the superconductivity of the hole-doped cuprates can be strongly suppressed at the so-called magic doping fractions. Despite great research efforts, the origin of the `magic doping' remains mysterious. Recently, we have developed a real-space theory of high-temperature superconductivity which reveals the intrinsic relationship between the localized Cooper pair and the localized hole pair (arXiv:1007.3536). Here we report that the theory can naturally explain the emergence of non-superconducting checkerboard phases and the magic doping problem in hole-doped cuprate superconductors. It clearly shows that there exist only seven `magic numbers' in the cuprate family at $x=$1/18, 1/16, 2/25, 1/9, 1/8, 2/9 and 1/4 with 6a*6a, 4a*4a, 5a*5a, 3a*3a, 4a*4a, 3a*3a and 2a*2a checkerboard patterns, respectively. Moreover, our framework leads directly to a satisfactory explanation of the most recent discovery [M. J. Lawler, et al. Nature 466, 347 (2010)] of the symmetries broken within each copper-oxide unit in hole-doped cuprate superconductors. These findings may shed new light on the mechanism of superconductivity.Comment: 5 pages, 6 figure

Detrended Structure-Function in Fully Developed Turbulence

The classical structure-function (SF) method in fully developed turbulence or for scaling processes in general is influenced by large-scale energetic structures, known as infrared effect. Therefore, the extracted scaling exponents $\zeta(n)$ might be biased due to this effect. In this paper, a detrended structure-function (DSF) method is proposed to extract scaling exponents by constraining the influence of large-scale structures. This is accomplished by removing a $1$st-order polynomial fitting within a window size $\ell$ before calculating the velocity increment. By doing so, the scales larger than $\ell$, i.e., $r\ge \ell$, are expected to be removed or constrained. The detrending process is equivalent to be a high-pass filter in physical domain. Meanwhile the intermittency nature is retained. We first validate the DSF method by using a synthesized fractional Brownian motion for mono-fractal processes and a lognormal process for multifractal random walk processes. The numerical results show comparable scaling exponents $\zeta(n)$ and singularity spectra $D(h)$ for the original SFs and DSFs. When applying the DSF to a turbulent velocity obtained from a high Reynolds number wind tunnel experiment with $Re_{\lambda}\simeq 720$, the 3rd-order DSF demonstrates a clear inertial range with $\mathcal{B}_3(\ell)\simeq 4/5\epsilon \ell$ on the range $10<\ell/\eta<1000$, corresponding to a wavenumber range $0.001<k\eta<0.1$. This inertial range is consistent with the one predicted by the Fourier power spectrum. The directly measured scaling exponents $\zeta(n)$ (resp. singularity spectrum $D(h)$) agree very well with a lognormal model with an intermittent parameter $\mu=0.33$. Due to large-scale effects, the results provided by the SFs are biased.Comment: 11 pages with 5 figures, accepted by Journal of Turbulenc

Adiabatic Decoherence-Free Subspaces and its Shortcuts

The adiabatic theorem and "shortcuts to adiabaticity" for the adiabatic dynamics of time-dependent decoherence-free subspaces are explored in this paper. Starting from the definition of the dynamical stable decoherence-free subspaces, we show that, under a compact adiabatic condition, the quantum state follows time-dependent decoherence-free subspaces (the adiabatic decoherence free subspaces) into the target subspace with extremely high purity, even though the dynamics of the quantum system may be non-adiabatic. The adiabatic condition mentioned in the adiabatic theorem is very similar with the adiabatic condition for closed quantum systems, except that the operators required to be "slowness" is on the Lindblad operators. We also show that the adiabatic decoherence-free subspaces program depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems has to be engineered according to the incoherent control program. Besides, "the shortcuts to adiabaticity" for the adiabatic decoherence-free subspaces program is also presented based on the transitionless quantum driving method. Finally, we provide an example of physical systems that support our programs. Our approach employs Markovian master equations and applies primarily to finite-dimensional quantum systems.Comment: 17 pages,5 figure

The SLOCC invariant and the residual entanglement for n-qubits

In this paper, we find the invariant for $n$-qubits and propose the residual entanglement for $n$-qubits by means of the invariant. Thus, we establish a relation between SLOCC entanglement and the residual entanglement. The invariant and the residual entanglement can be used for SLOCC entanglement classification for $n$-qubits.Comment: 22 pages, no figure, lemma 4 and corollary 3 and the conjecture for odd n-qubits in the previous version were deleted because they are not always tru

Multilevel quantum Otto heat engines with identical particles

A quantum Otto heat engine is studied with multilevel identical particles trapped in one-dimensional box potential as working substance. The symmetrical wave function for Bosons and the anti-symmetrical wave function for Fermions are considered. In two-particle case, we focus on the ratios of $W^i$ ($i=B,F$) to $W_s$, where $W^B$ and $W^F$ are the work done by two Bosons and Fermions respectively, and $W_s$ is the work output of a single particle under the same conditions. Due to the symmetric of the wave functions, the ratios are not equal to $2$. Three different regimes, low temperature regime, high temperature regime, and intermediate temperature regime, are analyzed, and the effects of energy level number and the differences between the two baths are calculated. In the multiparticle case, we calculate the ratios of $W^i_M/M$ to $W_s$, where $W^i_M/M$ can be seen as the average work done by a single particle in multiparticle heat engine. For other working substances whose energy spectrum have the form of $E_n\sim n^2$, the results are similar. For the case $E_n\sim n$, two different conclusions are obtained