scholarly journals Transport exponents of states with large support

2019 ◽  
Vol 31 (09) ◽  
pp. 1950029
Author(s):  
Vitalii Gerbuz
Keyword(s):  
Time Evolution ◽  
Quantum States ◽  
Single Site ◽  
Finite Support ◽  
Polymer Model ◽  
One Dimensional ◽  
Random Polymer ◽  
Initial States ◽  
Spreading Rates

We investigate spreading rates of one-dimensional quantum states under the Schrödinger time-evolution. The focus of this paper is on the states that either have finite support or decay exponentially at [Formula: see text]. In particular, we extend results of Damanik and Tcheremchantsev on estimating transport exponents that were originally proved to hold for the initial states supported on a single site. These general upper and lower estimates are then applied to several classes of models, including Sturmian, quasi-periodic and substitution-generated potentials, and the random polymer model.

Time evolution and thermalization of an ideal gas in a box

1977 ◽  
Vol 55 (3) ◽  
pp. 189-193
Author(s):  
H. J. Kreuzer ◽  
R. Teshima
Keyword(s):  
Time Evolution ◽  
Ideal Gas ◽  
Thermal Motion ◽  
One Dimensional

We study the time evolution of a gas of particles enclosed in a one-dimensional box the walls of which are in random thermal motion.

scholarly journals Tunable super- and subradiant boundary states in one-dimensional atomic arrays

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Anwei Zhang ◽  
Luojia Wang ◽  
Xianfeng Chen ◽  
Vladislav V. Yakovlev ◽  
Luqi Yuan
Keyword(s):  
Long Range ◽  
Quantum States ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Metrology ◽  
One Dimensional ◽  
Topological Quantum ◽  
Long Range Interactions ◽  
Boundary States ◽  
Quantum Optical

AbstractEfficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. Recently, atomic arrays have been shown to be a promising system for exploring topological quantum optics and robust control of quantum states, where the inherent nonlinearity is included through long-range hoppings. Here we show that a one-dimensional atomic array in a periodic magnetic field exhibits characteristic properties associated with an effective two-dimensional Hofstadter-butterfly-like model. Our work points out super- and sub-radiant topological edge states localized at the boundaries of the atomic array despite featuring long-range interactions, and opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions.

MAGNETO-CONTROLLING QUANTUM STATES OF A SINGLE PARTICLE INTERACTING WITH A SQUARE BARRIER

2008 ◽  
Vol 22 (12) ◽  
pp. 1231-1241
Author(s):  
QIONG CHEN ◽  
KUO HAI ◽  
WENHUA HAI
Keyword(s):  
Theoretical Analysis ◽  
Single Particle ◽  
Quantum Wire ◽  
Lower Energy ◽  
Magnetic Trap ◽  
Quantum States ◽  
Series Solutions ◽  
One Dimensional ◽  
Barrier Region ◽  
D Values

We obtain the exact solutions of a single particle magneto-confined in a one-dimensional (1D) quantum wire with a single square barrier. Theoretical analysis and numerical computation show that for a set of fixed barrier height and width, the quantum levels and states of the system depend on the displacement d of the magnetic trap, and for a fixed d value the system occupies only one or two lower quantum levels of n ≤ 20 of a free harmonic oscillator. In the barrier region, the finite-sized effect implies that only for some discrete barrier parameters and d values, the system has the Hermitian polynomial solutions, otherwise it has the infinite series solutions. Therefore, one can manipulate the external motional states of the system and prepare some required lower energy states by adjusting the displacement of the magnetic trap experimentally.

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