arXiv subjects

Damian Draxler

Publications and source records attributed to Damian Draxler.

3 recordsLinked to original sources

arXiv2017

Quantum Gross-Pitaevskii Equation

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

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arXiv2017

Continuous matrix product states with periodic boundary conditions and an application to atomtronics

We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system - an interacting Bose gas rotating in a ring shaped trap in the presence of a localised barrier potential.

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arXiv2013

Particles, holes and solitons: a matrix product state approach

We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excelent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's Type II excitation. In addition, a non-integrable model is introduced where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a non-trivial bound-state excitation in the dispersion relation.

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