Numerically-Exact Schrödinger Dynamics of Closed and Open Many-Boson Systems with the MCTDHB Package

The quantum many-body dynamics of indistinguishable, interacting particles are described by the time-dependent many-body Schrodinger equation (TDSE). The TDSE constitutes a difficult problem and is not solvable analytically in most cases. The present review article expedites and benchmarks the capabilities of a novel theoretical method, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) that is designed for solving the TDSE of interacting bosonic particles. The MCTDHB package is a software implementation that solves the equations of motion of MCTDHB numerically. It is assessed with a benchmark versus an analytically treatable model of trapped interacting bosons (a closed system) that the MCTDHB is capable of solving the TDSE for bosons numerically exactly, i.e., to any desired numerical precision. Furthermore, the structure and parallelization of the MCTDHB package as well as an application to the tunneling to open space dynamics [Proc. Natl. Acad. Sci. USA, 109, 13521 (2012)] are discussed.

[1]  L. Cederbaum,et al.  General mapping for bosonic and fermionic operators in Fock space , 2009, 0910.2577.

[2]  L. Cederbaum,et al.  How an interacting many-body system tunnels through a potential barrier to open space , 2012, Proceedings of the National Academy of Sciences.

[3]  L. Cederbaum,et al.  Exact quantum dynamics of a bosonic Josephson junction. , 2009, Physical review letters.

[4]  C. Wieman,et al.  Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor , 1995, Science.

[5]  J. Dalibard,et al.  Many-Body Physics with Ultracold Gases , 2007, 0704.3011.

[6]  Alessandro Silva,et al.  Colloquium: Nonequilibrium dynamics of closed interacting quantum systems , 2010, 1007.5331.

[7]  L. Cederbaum,et al.  Two trapped particles interacting by a finite-range two-body potential in two spatial dimensions , 2012, 1210.6701.

[8]  Lorenz S. Cederbaum,et al.  Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems , 2007, cond-mat/0703237.

[9]  L. Cohen,et al.  Exact reduced density matrices for a model problem , 1985 .

[10]  L. Cederbaum,et al.  Role of excited states in the splitting of a trapped interacting Bose-Einstein condensate by a time-dependent barrier. , 2006, Physical review letters.

[11]  L. Cederbaum,et al.  Recursive formulation of the multiconfigurational time-dependent Hartree method for fermions, bosons and mixtures thereof in terms of one-body density operators , 2011, 1109.4429.

[12]  Lorenz S. Cederbaum,et al.  Wave chaos as signature for depletion of a Bose-Einstein condensate , 2012, 1202.5869.

[13]  K. B. Davis,et al.  Bose-Einstein Condensation in a Gas of Sodium Atoms , 1995, EQEC'96. 1996 European Quantum Electronic Conference.

[14]  H. Meyer,et al.  Exact decay and tunnelling dynamics of interacting few-boson systems , 2009 .

[15]  L. Cederbaum,et al.  Excitation spectra of fragmented condensates by linear response: General theory and application to a condensate in a double-well potential , 2012, 1201.0714.

[16]  A. Streltsov.  Quantum systems of ultracold bosons with customized interparticle interactions , 2013, 1307.5187.

[17]  L. Cederbaum,et al.  Reduced Density Matrices and Coherence of Trapped Interacting Bosons , 2008, 0802.3417.

[18]  Jun Yan.  Harmonic Interaction Model and Its Applications in Bose–Einstein Condensation , 2003 .

[19]  F. Dalfovo,et al.  Theory of Bose-Einstein condensation in trapped gases , 1998, cond-mat/9806038.

[20]  L. Cederbaum,et al.  Accurate multi-boson long-time dynamics in triple-well periodic traps , 2009, 0910.5916.

[21]  L. Cederbaum,et al.  Numerically exact quantum dynamics of bosons with time-dependent interactions of harmonic type , 2012, 1207.5128.

[22]  Bradley,et al.  Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions. , 1995, Physical review letters.

[23]  A. Leggett,et al.  Bose-Einstein condensation in the alkali gases: Some fundamental concepts , 2001 .