Related papers: Density Matrix Geometry and Sum Rules
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
Recently, the gravitational polarization of the quantum vacuum was proposed as alternative to the dark matter paradigm. In the present paper we consider four benchmark measurements: the universality of the central surface density of galaxy…
We show that the equation of motion of scalar-tensor theory acquires thermodynamic identity when projected on a generic null surface. The relevant projection is given by $E_{ab}l^ak^b$, where $E_{ab} =8\pi T_{ab}^{(m)}$ represents the…
In this paper, a new representation of the Wigner function for a quantum system in the phase space is proposed. The new representation is of the form $W=\operatorname{Sp}\left[ \rho \mathcal{W} \right]$, where $\rho$ is the density matrix,…
We extend the results on decoherence in the thermodynamic limit [M. Frasca, Phys. Lett. A {\bf 283}, 271 (2001)] to general Hamiltonians. It is shown that N independent particles, initially properly prepared, have a set of observables…
We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model…
A geometrically nonlinear theory for field dislocation thermomechanics based entirely on measurable state variables is proposed. Instead of starting from an ordering-dependent multiplicative decomposition of the total deformation gradient…
We analyze the quantum melting of two-dimensional Wigner molecules (WM) in confined geometries with distinct symmetries and compare it with corresponding thermal melting. Our findings unfold complementary mechanisms that drive the quantum…
Effective theories of quantum liquids (superconductors and superfluids of various types) are derived starting from microscopic models at the absolute zero of temperature. Special care is taken to assure Galilei invariance. The effective…
We present a comprehensive theoretical analysis of the General Standard Model (GSM), a recently proposed framework that unifies particle physics and cosmology within the Gravitational Quantum Field Theory (GQFT). Constructed from first…
Noncommutative geometry is based on an idea that an associative algebra can be regarded as "an algebra of functions on a noncommutative space". The major contribution to noncommutative geometry was made by A. Connes, who, in particular,…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
The geometric characteristics of Bloch wave functions play a crucial role in electronic transport properties. We show that the thermoelectric performance of materials is governed by the geometric structure of Bloch wave functions within the…
We review the linear response theory in the horizontal quantum liquids framework spanning from Coulomb liquids to Atomic gases. There are several well known references about this subject, like the onset of the Kramers-Kronig relations and…
Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems,…
Generalized ideas of unified dark matter and dark energy in the context of dynamical space time theories with a diffusive transfer of energy are studied. The dynamical space-time theories are introduced a vector field whose equation of…
An important yet perplexing result from work in the 90s and 00s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was done by way of…
The technique of Weinberg's spectral-function sum rule is a powerful tool for a study of models in which global symmetry is dynamically broken. It enables us to convert information on the short-distance behavior of a theory to relations…
The quantum geometry plays a crucial role in the nonlinear transport of quantum materials. Here, we use the Boltzmann transport formalism to study the magnetic control of nonlinear transport induced by the quantum metric in two-dimensional…
In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological models in Gauss-Bonnet gravity with the boundary of the universe is assumed to be enclosed by the dynamical apparent…