Solution of the v-representability problem on a ring domain
- URL: http://arxiv.org/abs/2312.07225v1
- Date: Tue, 12 Dec 2023 12:41:10 GMT
- Title: Solution of the v-representability problem on a ring domain
- Authors: Sarina M. Sutter, Markus Penz, Michael Ruggenthaler, Robert van
Leeuwen, Klaas J. H. Giesbertz
- Abstract summary: We provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a ring domain.
Importantly, this allows for a well-defined Kohn-Sham procedure but, on the other hand, invalidates the usual proof of the Hohenberg-Kohn theorem.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We provide a solution to the v-representability problem for a
non-relativistic quantum many-particle system on a ring domain in terms of
Sobolev spaces and their duals. Any one-particle density that is
square-integrable, has a square-integrable weak derivative, and is gapped away
from zero can be realized from the solution of a many-particle Schr\"odinger
equation, with or without interactions, by choosing a corresponding external
potential. This potential can contain a distributional contribution but still
gives rise to a self-adjoint Hamiltonian. Importantly, this allows for a
well-defined Kohn-Sham procedure but, on the other hand, invalidates the usual
proof of the Hohenberg-Kohn theorem.
Related papers
- Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay.
We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
arXiv Detail & Related papers (2024-05-27T16:11:39Z) - Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism [55.2480439325792]
We analytically derive the modified Langevin noise formalism from the established canonical quantization of the electromagnetic field in macroscopic media.
We prove that each of the two field parts can be expressed in term of particular bosonic operators, which in turn diagonalize the electromagnetic Hamiltonian.
arXiv Detail & Related papers (2024-04-07T14:37:04Z) - 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) - The Harmonic Oscillator Potential Perturbed by a Combination of Linear and Non-linear Dirac Delta Interactions with Application to Bose-Einstein Condensation [0.0]
We study the bound state analysis of a one dimensional nonlinear version of the Schr"odinger equation.
We propose that the many-body interactions of the Bose gas can be effectively described by the nonlinear term in the Schr"odinger equation.
arXiv Detail & Related papers (2024-02-03T14:33:29Z) - The Schr\"odinger equation for the Rosen-Morse type potential revisited
with applications [0.0]
We rigorously solve the time-independent Schr"odinger equation for the Rosen-Morse type potential.
The resolution of this problem is used to show that the kinks of the non-linear Klein-Gordon equation with $varphi2p+2$ type potentials are stable.
arXiv Detail & Related papers (2023-04-12T18:43:39Z) - Exact solution for the interaction of two decaying quantized fields [0.9449650062296824]
We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schr"odinger equation and an effective non-Hermitian Hamiltonian.
This may be achieved by a non-unitary transformation that involves superoperators.
We may diagonalize the effective non-Hermitian Hamiltonian to obtain the evolution of any input state in a fully quantum domain.
arXiv Detail & Related papers (2023-04-12T02:05:14Z) - 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) - Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables.
In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z) - The presence of non-analyticities and singularities in the wavefunction
and the role of invisible delta potentials [0.0]
We identify the correct differential equation for a divergent square-integrable solution.
We infer that the divergent wavefunction would be caused by the potential V(r)=-r(r)
Because of its peculiar form and the fact that it leads to a divergent potential energy V> = infinity, the potential V(r) and the divergent wavefunction associated with it are not physically meaningful.
arXiv Detail & Related papers (2020-11-30T23:37:00Z) - Integrability of $1D$ Lindbladians from operator-space fragmentation [0.0]
We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems.
We show that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimension.
arXiv Detail & Related papers (2020-09-24T15:10:43Z)
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.