Quantum Mechanics
http://hdl.handle.net/20.500.11824/17
Thu, 19 May 2022 05:58:10 GMT2022-05-19T05:58:10ZEntanglement of classical and quantum short-range dynamics in mean-field systems
http://hdl.handle.net/20.500.11824/1438
Entanglement of classical and quantum short-range dynamics in mean-field systems
Bru, J. B.; de Siqueira Pedra, W.
The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed (Bru and de Siqueira Pedra, 0000; Bru and de Siqueira Pedra, 2021 [46,47]) the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) suppression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new.
Mon, 01 Nov 2021 00:00:00 GMThttp://hdl.handle.net/20.500.11824/14382021-11-01T00:00:00ZHigh temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph
http://hdl.handle.net/20.500.11824/1363
High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph
Zied, A.; Ratsimanetrimanana, A.
The Kubo-Martin-Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and Verboven, proposed an analogue to the KMS condition for infinite classical mechanical systems and highlighted its relationship with the Kirkwood-Salzburg equations and with the Gibbs equilibrium measures. In this paper, we prove that in a certain limiting regime of high temperature the classical KMS condition can be derived from the quantum condition in the simple case of the Bose-Hubbard dynamical system on a finite graph. The main ingredients of the proof are Golden-Thompson inequality, Bogoliubov inequality and semiclassical analysis.
Sun, 01 Aug 2021 00:00:00 GMThttp://hdl.handle.net/20.500.11824/13632021-08-01T00:00:00ZAnother Proof of Born's Rule on Arbitrary Cauchy Surfaces
http://hdl.handle.net/20.500.11824/1352
Another Proof of Born's Rule on Arbitrary Cauchy Surfaces
LIll, S.; Tumulka, R.
In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born's rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $\Sigma$, then the observed particle configuration on $\Sigma$ is a random variable with distribution density $|\Psi_\Sigma|^2$, suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.
Thu, 14 Oct 2021 00:00:00 GMThttp://hdl.handle.net/20.500.11824/13522021-10-14T00:00:00ZMacroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model
http://hdl.handle.net/20.500.11824/1292
Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model
Bru, J.-B.; de Siqueira Pedra, W.
The aim of the current paper is to illustrate, in a simple example, our
recent, very general, rigorous results
on the dynamical properties of fermions and quantum-spin systems with
long-range, or mean-field, interactions, in infinite volume. We consider
here the strong-coupling BCS-Hubbard model, because this example is very pedagogical and,
at the same time, physically relevant for it highlights the impact of the
(screened) Coulomb repulsion on ($s$-wave) superconductivity.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/20.500.11824/12922020-01-01T00:00:00Z