18,444 research outputs found
Low dimensional manifolds for exact representation of open quantum systems
Weakly nonlinear degrees of freedom in dissipative quantum systems tend to
localize near manifolds of quasi-classical states. We present a family of
analytical and computational methods for deriving optimal unitary model
transformations based on representations of finite dimensional Lie groups. The
transformations are optimal in that they minimize the quantum relative entropy
distance between a given state and the quasi-classical manifold. This naturally
splits the description of quantum states into quasi-classical coordinates that
specify the nearest quasi-classical state and a transformed quantum state that
can be represented in fewer basis levels. We derive coupled equations of motion
for the coordinates and the transformed state and demonstrate how this can be
exploited for efficient numerical simulation. Our optimization objective
naturally quantifies the non-classicality of states occurring in some given
open system dynamics. This allows us to compare the intrinsic complexity of
different open quantum systems.Comment: Added section on semi-classical SR-latch, added summary of method,
revised structure of manuscrip
Remarks on the notion of quantum integrability
We discuss the notion of integrability in quantum mechanics. Starting from a
review of some definitions commonly used in the literature, we propose a
different set of criteria, leading to a classification of models in terms of
different integrability classes. We end by highlighting some of the expected
physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and Kolmogorov complexity per
symbol are related by a theorem of Brudno. In this paper, we prove a quantum
version of this theorem, connecting the von Neumann entropy rate and two
notions of quantum Kolmogorov complexity, both based on the shortest qubit
descriptions of qubit strings that, run by a universal quantum Turing machine,
reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in
the Communications in Mathematical Physics
(http://www.springerlink.com/content/1432-0916/
Exact Matrix Product States for Quantum Hall Wave Functions
We show that the model wave functions used to describe the fractional quantum
Hall effect have exact representations as matrix product states (MPS). These
MPS can be implemented numerically in the orbital basis of both finite and
infinite cylinders, which provides an efficient way of calculating arbitrary
observables. We extend this approach to the charged excitations and numerically
compute their Berry phases. Finally, we present an algorithm for numerically
computing the real-space entanglement spectrum starting from an arbitrary
orbital basis MPS, which allows us to study the scaling properties of the
real-space entanglement spectra on infinite cylinders. The real-space
entanglement spectrum obeys a scaling form dictated by the edge conformal field
theory, allowing us to accurately extract the two entanglement velocities of
the Moore-Read state. In contrast, the orbital space spectrum is observed to
scale according to a complex set of power laws that rule out a similar
collapse.Comment: 10 pages and Appendix, v3 published versio
- …