Uncertainty relations for the Hohenberg-Kohn theorem
- URL: http://arxiv.org/abs/2010.01656v3
- Date: Wed, 27 Apr 2022 02:31:56 GMT
- Title: Uncertainty relations for the Hohenberg-Kohn theorem
- Authors: Purnima Ghale
- Abstract summary: The Hohenberg-Kohn theorem for non-relativistic, interacting many-body Schr"odinger systems is well-known.
However, the physical mechanism or principle which enables this theorem in nature has not been understood.
Here, we obtain effective canonical operators in the interacting many-body problem.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: How does charge density constrain many-body wavefunctions in nature? The
Hohenberg-Kohn theorem for non-relativistic, interacting many-body
Schr\"odinger systems is well-known and was proved using
\emph{reductio-ad-absurdum}; however, the physical mechanism or principle which
enables this theorem in nature has not been understood. Here, we obtain
effective canonical operators in the interacting many-body problem -- (i) the
local electric field, which mediates interaction between particles, and
contributes to the potential energy; and (ii) the particle momenta, which
contribute to the kinetic energy. The commutation of these operators results in
the charge density distribution. Thus, quantum fluctuations of interacting
many-particle systems are constrained by charge density, providing a mechanism
by which an external potential, by coupling to the charge density, tunes the
quantum-mechanical many-body wavefunction. As an initial test, we obtain the
functional form for total energy of interacting many-particle systems, and in
the uniform density limit, find promising agreement with Quantum Monte Carlo
simulations.
Related papers
- A non-hermitean momentum operator for the particle in a box [49.1574468325115]
We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example.
The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
arXiv Detail & Related papers (2024-03-20T12:51:58Z) - Energetics of the dissipative quantum oscillator [22.76327908349951]
We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap.
Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy.
We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
arXiv Detail & Related papers (2023-10-05T15:18:56Z) - Dilute neutron star matter from neural-network quantum states [58.720142291102135]
Low-density neutron matter is characterized by the formation of Cooper pairs and the onset of superfluidity.
We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and reconfiguration techniques.
arXiv Detail & Related papers (2022-12-08T17:55:25Z) - Formation of robust bound states of interacting microwave photons [148.37607455646454]
One of the hallmarks of interacting systems is the formation of multi-particle bound states.
We develop a high fidelity parameterizable fSim gate that implements the periodic quantum circuit of the spin-1/2 XXZ model.
By placing microwave photons in adjacent qubit sites, we study the propagation of these excitations and observe their bound nature for up to 5 photons.
arXiv Detail & Related papers (2022-06-10T17:52:29Z) - Correspondence Between the Energy Equipartition Theorem in Classical
Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed.
We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z) - Equivalence of dissipative and dissipationless dynamics of interacting
quantum systems with its application to the unitary Fermi gas [0.0]
We analytically study quantum dissipative dynamics described by the Caldirola-Kanai model with inter-particle interactions.
We have found that the dissipative quantum dynamics of the Caldirola-Kanai model can be exactly mapped to a dissipationless quantum dynamics under a negative external harmonic potential.
arXiv Detail & Related papers (2021-06-25T13:18:03Z) - Evolution of a Non-Hermitian Quantum Single-Molecule Junction at
Constant Temperature [62.997667081978825]
We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments.
We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
arXiv Detail & Related papers (2021-01-21T14:33:34Z) - Quantum Origins of the Density Operator [0.0]
Students in quantum mechanics are taught that the wave function contains all knowable information about an isolated system.
This paper brings attention to the fact that the density matrix can be reconciled with the underlying quantum-mechanical description.
arXiv Detail & Related papers (2020-12-25T00:24:28Z) - Bose-Fermi dualities for arbitrary one-dimensional quantum systems in
the universal low energy regime [0.2741266294612775]
I consider general interacting systems of quantum particles in one spatial dimension.
These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof.
The single-particle dispersion can be Galilean (non-relativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories.
arXiv Detail & Related papers (2020-09-01T18:00:04Z) - Many-body quantum dynamics slows down at low density [5.691318972818067]
We study quantum many-body systems with a global U(1) conservation law.
We define an effective operator size at finite chemical potential.
We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - Force and pressure in many-particle quantum dynamics [0.0]
We show that the quantum kinetic force between parts of an extended quantum system can be described by an operator acting on the boundary between the two subsystems.
The contribution to the force due to a short-ranged particle interaction can also be treated in the same way.
arXiv Detail & Related papers (2020-06-14T18:49:04Z)
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.