Dynamics of Quantum Coherence and Quantum Fisher Information After Sudden Quench

The dynamics of relative entropy and $l_{1}$-norm of coherence, as well as, the Wigner-Yanase-skew and quantum Fisher information are studied for a time-dependent coupled XY spin chain in presence of a time-dependent transverse magnetic field. Independent of the initial state of the system and while the relative entropy of coherence, $l_{1}$-norm of coherence, and quantum Fisher information are incapable, surprisingly, the dynamic Wigner-Yanase-skew information can truly spotlight the equilibrium critical point. We also observe that when the system is quenched to the critical point, these quantities show suppressions and revivals. Moreover, the first suppression (revival) time scales linearly with the system size and its scaling ratio is unique for all quenches independent to the initial phase. This is the promised universality of the first suppression (revival) time.Comment: 8 pages, 8 figures; to appear in Phys. Rev.

Disordered Kitaev chain with long-range pairing: Loschmidt echo revivals and dynamical phase transitions

We explore the dynamics of long-range Kitaev chain by varying pairing interaction exponent, $\alpha$. It is well known that distinctive characteristics on the nonequilibrium dynamics of a closed quantum system are closely related to the equilibrium phase transitions. Specifically, the return probability of the system to its initial state (Loschmidt echo), in the finite size system, is expected to exhibit very nice periodicity after a sudden quench to a quantum critical point. Where the periodicity of the revivals scales inversely with the maximum of the group velocity. We show that, contrary to expectations, the periodicity of the return probability breaks for a sudden quench to the non-trivial quantum critical point. Further, We find that, the periodicity of return probability scales inversely with the group velocity at the gap closing point for a quench to the trivial critical point of truly long-range pairing case, $\alpha < 1$. In addition, analyzing the effect of averaging quenched disorder shows that the revivals in the short range pairing cases are more robust against disorder than that of the long rang pairing case. We also study the effect of disorder on the non-analyticities of rate function of the return probability which introduced as a witness of the dynamical phase transition. We exhibit that, the non-analyticities in the rate function of return probability are washed out in the presence of strong disorders.Comment: 13+ pages, 8 figures, new results adde

Groups of Order 2048 with Three Generators and Three Relations

It is shown that there are exactly seventy-eight 3-generator 2- groups of order 2^11 with trivial Schur multiplier. We then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero

Real space renormalization of Majorana fermions in quantum nano-wire superconductors

We have applied the real space quantum renormalization group approach to study the topological quantum phase transition in the one-dimensional chain of a spinless p-wave superconductor. We investigate the behavior of local compressibility and ground-state fidelity of the Kitaev chain. We show that the topological phase transition is signaled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point have been used as a proper indicators for the topological quantum phase transition, which signals the appearance of Majorana fermions. We also present the scaling analysis of ground-state fidelity near the critical point that manifests the universal information about the topological phase transition.Comment: 7 pages, 9 figures; to appear in Journal of the Physical Society of Japan (JPSJ

Quantum filter for a class of non-Markovian quantum systems

In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorenztian noise. An ancillary system is introduced to convert white noise into Lorentzian noise which is injected into a principal system via a direct interaction. The resulting dynamics of the principal system are non-Markovian, which are driven by the Lorentzian noise. By probing the principal system, a quantum filter for the augmented system can be derived from standard theory, where the conditional state of the principal system can be obtained by tracing out the ancillary system. An example is provided to illustrate the non-Markovian dynamics of the principal system.Comment: 8 pages, 7 figure

Quantum filter for a non-Markovian single qubit system

In this paper, a quantum filter for estimating the states of a non-Markovian qubit system is presented in an augmented Markovian system framework including both the qubit system of interest and multi-ancillary systems for representing the internal modes of the non-Markovian environment. The colored noise generated by the multi-ancillary systems disturbs the qubit system via a direct interaction. The resulting non-Markovian dynamics of the qubit is determined by a memory kernel function arising from the dynamics of the ancillary system. In principle, colored noise with arbitrary power spectrum can be generated by a combination of Lorentzian noises. Hence, the quantum filter can be constructed for the qubit disturbed by arbitrary colored noise and the conditional state of the qubit system can be obtained by tracing out the multi-ancillary systems. An illustrative example is given to show the non-Markovian dynamics of the qubit system with Lorentzian noise.Comment: arXiv admin note: text overlap with arXiv:1503.0799