|
| related topics |
| {phase, path, phys} |
| {group, space, representation} |
| {state, states, coherent} |
| {time, wave, function} |
| {classical, space, random} |
| {equation, function, exp} |
| {spin, pulse, spins} |
| {energy, gaussian, time} |
| {cos, sin, state} |
| {vol, operators, histories} |
| {temperature, thermal, energy} |
| {operator, operators, space} |
| {bell, inequality, local} |
| {energy, state, states} |
| {let, theorem, proof} |
|
Coherent-state path integral calculation of the Wigner function
J H Samson
abstract: We consider a set of operators hat{x}=(hat{x}_1,..., hat{x}_N) with diagonal
representatives P(n) in the space of generalized coherent states |n>;
hat{x}=int dn P(n) |n>_L over polygonal paths with L vertices
{n_1...L}. The distribution of the path centroid bar{P}=(1/L)
sum_{i=1}^{L}P(n_i) tends to the Wigner function W(x), the joint distribution
for the operators: W(x)=lim_{L->infinity} _{L}. This result is
proved in the case where the Hamiltonian commutes with hat{x}. The Wigner
function is non-positive if the dominant paths with path centroid in a certain
region have Berry phases close to odd multiples of pi. For finite L the path
centroid distribution is a Wigner function convolved with a Gaussian of
variance inversely proportional to L. The results are illustrated by numerical
calculations of the spin Wigner function from SU(2) coherent states. The
relevance to the quantum Monte Carlo sign problem is also discussed.
- oai_identifier:
- oai:arXiv.org:quant-ph/0006021
- categories:
- quant-ph math-ph math.MP
- comments:
- 12 pages, 2 figures, to appear J Phys A. Requires IOP style files
- doi:
- 10.1088/0305-4470/33/29/306
- arxiv_id:
- quant-ph/0006021
- created:
- 2000-06-05
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