Two-dimensional Bloch oscillations: a Lie-algebraic approach

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.

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Bloch oscillations in two-dimensional lattices

New Journal of Physics ◽

10.1088/1367-2630/6/1/041 ◽

2004 ◽

Vol 6 ◽

pp. 41-41 ◽

Cited By ~ 31

Author(s):

D Witthaut ◽

F Keck ◽

H J Korsch ◽

S Mossmann

Keyword(s):

Two Dimensional ◽

Bloch Oscillations

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Optical Bloch oscillations and Zener tunneling in two-dimensional photonic lattices

Nonlinear Guided Waves and Their Applications ◽

10.1364/nlgw.2005.thd1 ◽

2005 ◽

Cited By ~ 1

Author(s):

Henrike Trompeter ◽

Wieslaw Krolikowski ◽

Dragomir N. Neshev ◽

Anton S. Desyatnikov ◽

Andrey A. Sukhorukov ◽

...

Keyword(s):

Two Dimensional ◽

Bloch Oscillations ◽

Photonic Lattices ◽

Zener Tunneling

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Algebraic approach to non-separable two-dimensional Schrödinger equation: Ground states for polynomial and Morse-like potentials

Open Physics ◽

10.2478/s11534-014-0484-5 ◽

2014 ◽

Vol 12 (10) ◽

Author(s):

Vladimír Tichý ◽

Lubomír Skála ◽

René Hudec

Keyword(s):

Schrödinger Equation ◽

Ground State ◽

Schrodinger Equation ◽

Ground States ◽

Algebraic Approach ◽

Algebraic Method ◽

Analytic Solutions ◽

Wave Functions ◽

Two Dimensional ◽

One Dimensional

AbstractThis paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.

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An algebraic approach to the waiting time process in GI/M/S

Journal of Applied Probability ◽

10.1017/s0021900200042182 ◽

1973 ◽

Vol 10 (01) ◽

pp. 181-191 ◽

Cited By ~ 1

Author(s):

Jacqueline Loris-Teghem

Keyword(s):

Waiting Time ◽

Algebraic Approach ◽

Markovian Process ◽

Time Process ◽

Two Dimensional ◽

Transient Behaviour ◽

Waiting Time Process ◽

The Times

The transient behaviour of the waiting time process in GI/M/S is studied algebraically by means of a two-dimensional Markovian process {(vn, ln } , where the variables vn denote the times of full occupation immediately after the arrival instants Tn and where ln = max {0,– 1 + number of idle servers at (Tn + 0)}.

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