Related papers: Symplectic Non-Squeezing Theorems, Quantization of…
We discuss the phase coherence properties of a mesoscopic normal ring coupled to an electric environment via Coulomb interactions. This system can be mapped onto the Caldeira-Leggett model with a flux dependent tunneling amplitude. We show…
In this work, we explore the implications of applying the formalism of symplectic geometry to quantum mechanics, particularly focusing on many-particle systems. We extend the concept of a symplectic indicator of entanglement, originally…
We investigate properties of the covariance matrix in the framework of non-commutative quantum mechanics for an one-parameter family of transformations between the familiar Heisenberg-Weyl algebra and a particular extension of it. Employing…
The recently proposed de Sitter swampland conjecture excludes local extrema of a scalar potential with a positive energy density in a low energy effective theory. Under the conjecture, the observed dark energy cannot be explained by the…
At the recent QSCP XIX, the author claimed a procedure of using a scaled Fourier transform (the scaling being determined by the detailed interaction and particle mass for a harmonic oscillator) to achieve simultaneous resolution of position…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a Hamiltonian dynamics in an intrinsic time $\tau$ which samples a…
The integrability of a quantum many-body system, which is characterized by the presence or absence of local conserved quantities, drastically impacts the dynamics of isolated systems, including thermalization. Nevertheless, a rigorous and…
An extension of the fundamental laws of thermodynamics and of the concept of entropy to the ground state fluctuations of the quantum fields is studied and some new results are found. At the end a device to extract energy from the vacuum…
Infinitesimal volumes stretch and contract as they coevolve with classical phase space trajectories according to linearized dynamics. Unless these tangent-space dynamics are modified, chaotic evolution causes the volume spanned by evolving…
We show that the infinite-dimensional representation of the recently introduced Logistic algebra can be interpreted as a non-trivial generalization of the Heisenberg or oscillator algebra. This allow us to construct a quantum Hamiltonian…
Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of…
The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant $\Lambda$ is zero. The resulting framework lies at the foundation of research in diverse…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…
We study the minimum volume ellipsoid estimator associates to a cloud of points in phase space. Using as a natural measure of uncertainty the symplectic capacity of the covariance ellipsoid we find that classical uncertainties obey…
We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. Generically, the larger the measured energy fluctuations are, the larger the entanglement is. Examples are…
This paper explains an application of Gromov's h-principle to prove the existence, on any orientable 4-manifold, of a folded symplectic form. That is a closed 2-form which is symplectic except on a separating hypersurface where the form…
We study the scaling limit of statistical mechanics models with non-convex Hamiltonians that are gradient perturbations of Gaussian measures. Characterising features of our gradient models are the imposed boundary tilt and the surface…
The Hamiltonian system of general relativity and its quantization without any matter or gauge fields are discussed on the basis of the symplectic geometrical theory. A symplectic geometry of classical general relativity is constructed using…
Hohenberg-Kohn (HK) theorem is a cornerstone of modern electronic structure calculations. For interacting electrons, given that the internal part of the Hamiltonian ($\hat H_{int}$), containing the kinetic energy and Couloumb interaction of…