相关论文: Density Matrix Geometry and Sum Rules

A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…

Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…

A new approach based on a statistical operator is presented, which allows to take into account the inhomogeneous particle distribution induced by gravitational interaction. This method uses the saddle point procedure to find the dominant…

We derive non-perturbative sum rules in SU($N$) lattice gauge theory at finite temperature. They relate the susceptibilities of the trace anomaly and energy-momentum tensor to temperature derivatives of the thermodynamic potentials. Two of…

We derive sum rules involving the spectral density of the stress-energy tensor in N=4 super-Yang-Mills theory and pure Yang-Mills theory. The sum rules come from the hydrodynamic behavior at small momenta and the conformal (in the case of…

Attempts to understand zero temperature phase transitions have forced physicists to consider a regime where the standard paradigms of condensed matter physics break down [1-4]. These quantum critical systems lack a simple description in…

We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no…

Gauge/gravity duality has proved to be a very successful tool for describing strongly coupled systems in particle physics and heavy ion physics. The application of the gauge/gravity duality to quantum matter is a promising candidate to…

Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo…

We consider sum rules of the Weinberg type at zero and nonzero temperatures. On the basis of the operator product expansion at zero temperature we obtain a new sum rule which involves the average of a four-quark operator on one side and…

We outline a fundamentally quantum description of bosonic dark matter (DM) from which the conventional classical-wave picture emerges in the limit $m \ll 10~\textrm{eV}$. As appropriate for a quantum system, we start from the density matrix…

We use the density matrix formalism in order to calculate the energy level shifts, in second order on interaction, of an atom in the presence of a perfectly conducting wall in the dipole approximation. The thermal corrections are also…

Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…

We resolve the long standing question of temperature dependence of uniformly moving bodies by means of a quantum statistical treatment centred on the zeroth law of thermodynamics. The key to our treatment is the result, established by…

We consider arbitrary quantum wire networks modelled by finite, noncompact, connected quantum graphs in the presence of an external magnetic field. We find a general formula for the total scattering matrix of the network in terms of its…

Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…

We study the symmetries of non-relativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the non-relativistic diffeomorphism…

The exact quantum integrability aspects of a sector of the membrane is investigated. It is found that spherical membranes moving in flat target spacetime backgrounds admit a class of integrable solutions linked to SU(infty) SDYM equations…

We present the time-dependent Quantum Geometric Tensor (tQGT) as a comprehensive tool for capturing the geometric character of insulators observable within linear response. We show that tQGT describes the zero-point motion of bound…

Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…