Related papers: Second Quantization and the Spectral Action
This paper is devoted to the numerical analysis of the Hermite spectral method proposed in [14], which provides, in the semiclassical limit, an asymptotic preserving approximation of the von Neumann equation. More precisely, it relies on…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
A functional integral representation is given for a large class of quantum mechanical models with a non--L2 ground state. As a prototype the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state…
We present first results on the calculation of fermionic spectral functions from analytically continued flow equations within the Functional Renormalization Group approach. Our method is based on the same analytic continuation from…
Using techniques proposed in [Sason, IEEE Trans. Inf. Th. 59, 7118 (2013)] and [Becker, Datta and Jabbour, IEEE Trans. Inf. Th. 69, 4128 (2023)], and based on the results from the latter, we construct a globally optimal continuity bound for…
We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the entropies of subsystems associated to…
Electromagnetism in substance is characterized by permittivity (dielectric constant) and permeability (magnetic permeability). They describe the substance property {\it effectively}. We present a {\it geometric} approach to it. Some models…
We present a method to obtain spectral functions at finite temperature from the Functional Renormalization Group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with analytically…
In a minimal 2-band model with attractive interactions between fermions, we calculate the gap to single and two-particle excitations, the band-dependent spectral functions, the superfluid density and compressibility using quantum Monte…
In the in-out formalism we advance a new method to represent the gamma function for QED actions in supercritical fields, which is complementary to the proper-time integral representation in Phys. Rev. D 78, 105013 (2008) and Phys. Rev. D…
For spectral actions consisting of the average number of particles and arising from open systems made of general free $q$-particles (including Bose, Fermi and classical ones corresponding to $q=\pm 1$ and $0$, respectively) in thermal…
We prove that in bosonic quantum mechanics the two-point spectral form factor can be obtained as an average of the two-point out-of-time ordered correlation function, with the average taken over the Heisenberg group. In quantum field…
A method is developed for realizing entanglement and general second quantized fermionic and bosonic fields in the framework of the fermionic projector.
We define zeta functions for the adjoint action of GL(n) on its Lie algebra and study their analytic properties. For n<4 we are able to fully analyse these functions, and recover the Shintani zeta function for the prehomogeneous vector…
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…
Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt…
We assess whether a confined Wigner molecule constituted by $2N$ fermions behaves as $N$ bosons or $2N$ fermions. Following the work by C. K. Law [Phys. Rev. A \textbf{71}, 034306 (2005)] and Chudzicki et al. [Phys. Rev. Lett. \textbf{104},…
The purpose of this paper is to present a quantum statistical theory of 2-dimensional vortex gas based on the generalized Hamiltonian dynamics recently developed. The quantized spectrum is evaluated for a pair of vortex on the basis of the…
We perform a theoretical study of a fermionic gas with two hyperfine states confined to an optical lattice. We derive a generic state diagram as a function of interaction strength, particle number, and confining potential. We discuss the…
The formalism of subdynamics is extended to the functional approach of quantum systems, and used for the Friedrichs model, in which diagonal singularities in states and observables are included. We compute in this approach the generalized…