Mott insulator-superfluid transition in a periodic lattice of Josephson junctions can be driven by tunneling rate increase. The resulting winding numbers $W$ of the condensate wave function decrease with increasing quench time in accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches, Bose-Hubbard dynamics rearranges the wave-function phase so that its random walk cools, $\overline{{W}^{2}}$ decreases and eventually the wave function becomes too cold to overcome potential barriers separating different $W$ . Thus, in contrast with KZM, in very slow quenches $\overline{{W}^{2}}$ is set by random walk with ``critical'' step size, independently of ${\ensuremath{\tau}}_{Q}$. As our study requires use of the truncated Wigner approximation (TWA) over relatively long time intervals, we investigate the validity of TWA by comparing its predictions with exact calculations for suitably small quantum systems.Mott insulator-superfluid transition in a periodic lattice of Josephson junctions can be driven by tunneling rate increase. The resulting winding numbers $W$ of the condensate wave function decrease with increasing quench time in accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches, Bose-Hubbard dynamics rearranges the wave-function phase so that its random walk cools, $\overline{{W}^{2}}$ decreases and eventually the wave function becomes too cold to overcome potential barriers separating different $W$. Thus, in contrast with KZM, in very slow quenches $\overline{{W}^{2}}$ is set by random walk with ``critical'' step size, independently of ${\ensuremath{\tau}}_{Q}$. As our study requires use of the truncated Wigner approximation (TWA) over relatively long time intervals, we investigate the validity of TWA by comparing its predictions with exact calculations for suitably small quantum systems.

arXiv:1103.0669Physical Review BSep 26, 20117 citations

Self-consistent theory of concentrational self-quenching

Evgeny N. Bodunov, Viktor A. Malyshev

OptSpJun 1, 19872 citations

Adjustable self-loop on discrete-time quantum walk and its application in spatial search

Huiquan Wang, Jie Zhou, Junjie Wu +1 more

How self-loops on vertices affect quantum walks is an interesting issue, and self-loops play important roles in quantum walk based algorithms. However, the original model that adjusting the effect of self-loops by changing their number has limitations. For example, the effect of self-loops cannot be adjusted continuously, for their number must be an integer. In this paper, we proposed a model of adjustable self-loop on discrete-time quantum walk, whose weight is controlled by a real parameter in the coin operator. The proposed method not only generalises the situations where the number of self-loops is an integer, but also provides a way to adjust the weight of the self-loop continuously. It enhances the potential of self-loops in applications. For instance, we improve the success rate of the quantum walk based search on a $20\times20$ two-dimension lattice from $23.6\%$ to $97.2\%$ by the proposed method. And the success rate of the improved search, which only scales as $O(1/\log{N})$ before being improved, even increases slightly with the size of the lattice. To the best of our knowledge, this is the first time that such an improvement is achieved on the quantum walk based spatial search.How self-loops on vertices affect quantum walks is an interesting issue, and self-loops play important roles in quantum walk based algorithms. However, the original model that adjusting the effect of self-loops by changing their number has limitations. For example, the effect of self-loops cannot be adjusted continuously, for their number must be an integer. In this paper, we proposed a model of adjustable self-loop on discrete-time quantum walk, whose weight is controlled by a real parameter in the coin operator. The proposed method not only generalises the situations where the number of self-loops is an integer, but also provides a way to adjust the weight of the self-loop continuously. It enhances the potential of self-loops in applications. For instance, we improve the success rate of the quantum walk based search on a $20\times20$ two-dimension lattice from $23.6\%$ to $97.2\%$ by the proposed method. And the success rate of the improved search, which only scales as $O(1/\log{N})$ before being improved, even increases slightly with the size of the lattice. To the best of our knowledge, this is the first time that such an improvement is achieved on the quantum walk based spatial search.

arXiv:1707.00601Jul 3, 20175 citations

Cooperative quenching kinetics: Computer simulation and analytical solution

Tasoltan T. Basiev, Konstantin K. Pukhov, Irina Basieva

Chemical Physics LettersOct 21, 20069 citations

Effect of trapping on transport coherence. II. Continuous-time random-walk treatment

Pavel Heřman, Ivan Barvı́k

Our recent investigation led to the conclusion that there is much agreement among theories of the excitation transfer: the generalized master equation (GME), the Haken-Strobl-Reineker stochastic-Liouville-equation theory, and the Grover-Silbey microscopic theory. Trapping effects influence memory functions entering the GME. Decoupling of the rest of the system from the sink in the nearly coherent regime for large trapping rates changes the form of the pausing-time-distribution functions and probability densities in the continuous-time random-walk method.Our recent investigation led to the conclusion that there is much agreement among theories of the excitation transfer: the generalized master equation (GME), the Haken-Strobl-Reineker stochastic-Liouville-equation theory, and the Grover-Silbey microscopic theory. Trapping effects influence memory functions entering the GME. Decoupling of the rest of the system from the sink in the nearly coherent regime for large trapping rates changes the form of the pausing-time-distribution functions and probability densities in the continuous-time random-walk method.

Physical review. B, Condensed matterAug 1, 19936 citations

Concentration quenching of noncoherent excitation in solutions

Anatoly I. Burshtein

Uspekhi Fizicheskih NaukJan 1, 198462 citations

Mott insulator-superfluid transition in a periodic lattice of Josephson junctions can be driven by tunneling rate increase. The resulting winding numbers

W

of the condensate wave function decrease with increasing quench time in accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches, Bose-Hubbard dynamics rearranges the wave-function phase so that its random walk cools,

\overline{{W}^{2}}

decreases and eventually the wave function becomes too cold to overcome potential barriers separating different

W

. Thus, in contrast with KZM, in very slow quenches

\overline{{W}^{2}}

is set by random walk with ``critical'' step size, independently of ${\ensuremath{\tau}}_{Q}$. As our study requires use of the truncated Wigner approximation (TWA) over relatively long time intervals, we investigate the validity of TWA by comparing its predictions with exact calculations for suitably small quantum systems.

20\times20

two-dimension lattice from

23.6\%

97.2\%

by the proposed method. And the success rate of the improved search, which only scales as

O(1/\log{N})

before being improved, even increases slightly with the size of the lattice. To the best of our knowledge, this is the first time that such an improvement is achieved on the quantum walk based spatial search.