相关论文: Density Matrix Geometry and Sum Rules

The geometric sum plays a significant role in risk theory and reliability theory \cite{Kala97} and a prototypical example of the geometric sum is R\'enyi's theorem~\cite{Renyi56} saying a sequence of suitably parameterised geometric sums…

I propose that the proper framework for gravitational scattering theory is the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and Shaw[1], and its generalizations. Certain representation spaces of these algebras…

The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…

Motivated by the normal state of the cuprates in which the f-sum rule increases faster than a linear function of the particle density, we derive a conductivity sum rule for a system in which the kinetic energy operator in the Hamiltonian is…

Quantum fluctuations of the vacuum stress-energy tensor are highly non-Gaussian, and can have unexpectedly large effects on spacetime geometry. In this paper, we study a two-dimensional dilaton gravity model coupled to a conformal field, in…

Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…

The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purification map), which is nonlinear map, is introduced. The density…

We study symmetric nuclear matter at finite temperature, with particular emphasis on the liquid-gas phase transition. We use a standard covariance analysis to propagate statistical uncertainties from the density functional to the…

I have shown that the field defined by the Wheeler-DeWitt equation for \textit{pure gravity} is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and…

We construct a random matrix model that, in the large $N$ limit, reduces to the low energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of…

Strongly correlated systems are often associated with an underlying quantum critical point which governs their behavior in the finite temperature phase diagram. Their thermodynamical and transport properties arise from critical fluctuations…

We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes…

Dimensionality is a fundamental concept in physics, which plays a hidden but crucial role in various domains, including condensed matter physics, relativity and string theory, statistical physics, etc. In quantum physics, reducing…

Jamming is a geometric phase transition occurring in dense particle systems in the absence of temperature. We use computer simulations to analyse the effect of thermal fluctuations on several signatures of the transition. We show that…

Attempts for a geometrical interpretation of Quantum Theory were made, notably the deBroglie-Bohm formulation. This was further refined by Santamato who invoked Weyl's geometry. However these attempts left a number of unanswered questions.…

A scalar-tensor theory of gravity is formulated in which $G$ and particle masses are allowed to vary. The theory yields a globally static cosmological model with no evolutionary timescales, no cosmological coincidences, and no flatness and…

Friedel's sum rule provides an explicit expression for a conductance functional, $\mathcal{G}[n]$, valid for the single impurity Anderson model at zero temperature. The functional is special because it does not depend on the interaction…

We study geometric properties of a random Gaussian short-time correlated velocity field by considering statistics of a passively advected metric tensor. That describes universal properties of fluctuations of tensor objects frozen into the…

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an…

A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by…