Confinement of $N$-body systems and non-integer dimensions
- URL: http://arxiv.org/abs/2403.06519v1
- Date: Mon, 11 Mar 2024 08:52:48 GMT
- Title: Confinement of $N$-body systems and non-integer dimensions
- Authors: E. Garrido and A.S. Jensen
- Abstract summary: The squeezing process of a three-dimensional quantum system can be described by the $d$-method, without external field and where the dimension can take non-integer values.
We first generalize both methods to $N$ particles and any transition between dimensions below $3$.
We have in all the cases found that the derived analytic relations between the two methods work very well.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: The squeezing process of a three-dimensional quantum system by use of an
external deformed one-body oscillator potential can also be described by the
$d$-method, without external field and where the dimension can take non-integer
values. In this work we first generalize both methods to $N$ particles and any
transition between dimensions below $3$. Once this is done, the use of harmonic
oscillator interactions between the particles allows complete analytic
solutions of both methods, and a direct comparison between them is possible.
Assuming that both methods describe the same process, leading to the same
ground state energy and wave function, an analytic equivalence between the
methods arises. The equivalence between both methods and the validity of the
derived analytic relation between them is first tested for two identical bosons
and for squeezing transitions from 3 to 2 and 1 dimensions, as well as from 2
to 1 dimension. We also investigate the symmetric squeezing from 3 to 1
dimensions of a system made of three identical bosons. We have in all the cases
found that the derived analytic relations between the two methods work very
well. This fact permits to relate both methods also for large squeezing
scenarios, where the brute force numerical calculation with the external field
is too much demanding from the numerical point of view, especially for systems
with more than two particles.
Related papers
- Numerical evaluation of orientation averages and its application to molecular physics [39.58317527488534]
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables.
We derive guidelines for choosing the best quadrature method for orientation averages.
We also present a Python package providing a flexible interface to a variety of quadrature methods.
arXiv Detail & Related papers (2024-07-24T17:09:41Z) - Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions.
We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
arXiv Detail & Related papers (2024-07-09T14:04:11Z) - Three-body Forces in Oscillator Bases Expansion [0.0]
The method is generalised to include the management of a given class of three-body forces.
The accuracy of the generalisation is assessed by comparing with results from Lagrange mesh method.
Extensions for systems of $N$ identical bodies and for systems of two identical particles and one distinct are also discussed.
arXiv Detail & Related papers (2024-05-28T13:50:20Z) - Hard confinement of a two-particle quantum system using the variational
method [0.0]
The method is used to study the hard confinement of a two-particle quantum system in two potential models.
The behavior of $|psi|2$, the wavefunction at the origin (WFO), and the mean radius $evr$ are computed for different situations.
arXiv Detail & Related papers (2024-02-16T16:12:08Z) - Theory of free fermions under random projective measurements [43.04146484262759]
We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers.
We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
arXiv Detail & Related papers (2023-04-06T15:19:33Z) - Tuning of Efimov states in non-integer dimensions [0.0]
We show that by combining Feshbach resonances with external confining potentials, the energy scale factor of neighboring Efimov states can be greatly reduced.
The results are universal as they only rely on large-distance properties.
arXiv Detail & Related papers (2023-03-07T12:20:47Z) - Correspondence between open bosonic systems and stochastic differential
equations [77.34726150561087]
We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment.
A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
arXiv Detail & Related papers (2023-02-03T19:17:37Z) - Two-body continuum states in non-integer geometry [0.0]
Wave functions, phase shifts and corresponding elastic cross sections are investigated for two short-range interacting particles in an external field.
We derive analytic expressions for scattering lengths and phase shifts using a square-well potential.
We show that the phase shifts are the same in both methods.
arXiv Detail & Related papers (2022-03-02T14:26:06Z) - Conditions for realizing one-point interactions from a multi-layer
structure model [77.34726150561087]
A heterostructure composed of $N$ parallel homogeneous layers is studied in the limit as their widths shrink to zero.
The problem is investigated in one dimension and the piecewise constant potential in the Schr"odinger equation is given.
arXiv Detail & Related papers (2021-12-15T22:30:39Z) - Random quantum circuits anti-concentrate in log depth [118.18170052022323]
We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated.
Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform.
In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
arXiv Detail & Related papers (2020-11-24T18:44:57Z) - Three identical bosons: Properties in non-integer dimensions and in
external fields [0.0]
Three-body systems that are continuously squeezed from a three-dimensional (3D) space into a two-dimensional (2D) space are investigated.
An alternative is provided by use of the dimension $d$ as a parameter that changes continuously within the range $2leq d leq 3$.
The simplicity of the $d$-calculations is exploited to investigate the evolution of three-body states after progressive confinement.
arXiv Detail & Related papers (2020-07-31T08:32:49Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.