In quantum mechanics, states are described by density matrices. Though their probabilistic interpretation is rooted in ensemble theory, matrices embody a known shortcoming. They do not completely express the physical realization of an ensemble. Conveniently, outcome statistics projective and positive operator-valued measurements depend on realization, only matrix. Here, we show how geometric ap...

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nùñez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for ...

By applying the supersymmetric approach we rigorously prove smoothness of the averaged density of states for a three dimensional random band matrix ensemble, in the limit of infinite volume and fixed band width. We also prove that the resulting expression for the density of states coincides with the Wigner semicircle with a precision 1/W , for W large but finite.