Spatial Non-locality in Confined Quantum Systems: A Liaison with Quantum Correlations
- PDF / 639,105 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 88 Downloads / 165 Views
Ivan P. Christov
Spatial Non-locality in Confined Quantum Systems: A Liaison with Quantum Correlations
Received: 8 August 2020 / Accepted: 17 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020, corrected publication 2020
Abstract Using advanced stochastic methods (time-dependent quantum Monte Carlo, TDQMC) we explore the ground state of 1D and 2D artificial atoms with up to six bosons in harmonic trap where these interact by long-range and short-range Coulomb-like potentials (bosonic quantum dots). It is shown that the optimized value of the key variational parameter in TDQMC named nonlocal correlation length is close to the standard deviation of the Monte Carlo sample for one boson and it is slightly dependent on the range of the interaction potential. Also it is almost independent on the number of bosons for the 2D system thus confirming that the spatial quantum non-locality experienced by each particle is close to the spatial uncertainty exhibited by the rest of the particles. The intimate connection between spatial non-locality and quantum correlations is clearly evidenced.
1 Introduction In classical physics, when measuring the position of a particle the measurement result corresponds to a certain location while in quantum mechanics the outcome is a whole set of possible locations. In the one-body case (e.g. in the hydrogen atom) the probability distribution of these locations is described by modulus square of the ground state wave function in coordinate representation which is of non-zero width because that state is not an eigenstate of the position operator [1]. In the many-body case, however, the wave function resides in configuration space which implies a mutual connection between the possible positions occupied by each particle with the positions of the rest of the particles, which evidences the quantum nonlocality and entanglement [2]. Using a Monte Carlo (MC) language one may assign an ensemble of finite number of point-like walkers to each physical particle where the standard deviation of the MC sample is a quantitative measure for how much uncertainty there is for that particle in coordinate space, as done in e.g. the variational quantum Monte Carlo (QMC) method, where a many-body trial wave function is sampled [3]. Other approaches to study fewparticle quantum systems include Gaussian variational [4,5] , hyperspherical [6], and stochastic variational method [7,8] which also employ optimized static many-body trial functions. However the use of static trial functions may not be sufficient for describing some essential properties of quantum systems which depend on the phase of the wave function e.g. for real-time dynamics. Within the MC methodology one possible way to overcome the exponential scaling imposed by the exact many-body wave function is to introduce in a selfconsistent manner an ensemble of wave-functions considered as random walkers in one-body Hilbert space for each particle, where each individual MC walker is guided by a corresponding wave-function (guide wave) i
Data Loading...
