Related papers: Subsets and the canonical partition functions
The equation of state of a system at equilibrium may be derived from the canonical or the grand canonical partition function. The former is a function of temperature T, while the latter also depends on the chemical potential \mu for…
We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic…
Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of…
We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an…
We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant…
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms of free fermionic operators. This…
In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of…
We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero…
The number partitioning problem is a classic problem of combinatorial optimization in which a set of $n$ numbers is partitioned into two subsets such that the sum of the numbers in one subset is as close as possible to the sum of the…
The phenomenon of dynamical quark mass generation is studied in QCD within the framework of a gauge invariant formalism. An exact relationship is established between the equation satisfied by the scalar part of the two-point gauge invariant…
Anomalous sector of chiral Lagrangian is calculated in a gauge invariant, nonlocal, dynamical quark model. The Wess-Zumino term is proved coming from two kinds of sources, one is independent on and another dependent on dynamical quark self…
We studied integration contour deformations in the chiral random matrix theory of Stephanov with the goal of alleviating the finite-density sign problem. We considered simple ans\"atze for the deformed integration contours, and optimized…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to…
We study solutions of a transcendental equation for the complex chemical potential at which a random-matrix QCD model can undergo a phase transition at zero mass. An explicit solution is obtained in terms of the Lambert W function. We also…
A $(2+1)$-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity…
We investigate the Euclidean path integral formulation of QCD at finite baryon density and temperature. We show that the partition function Z can be written as a difference between two sums Z+ and Z-, each of which defines a partition…
We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of $\mathrm{PSL}(2,\mathbb{R})$ Chern-Simons theory and is simpler to treat in…
The coupling of spin 0 and spin 1 external fields to Dirac fermions defines a theory which displays gauge chiral symmetry. Quantum mechanically, functional integration of the fermions yields the determinant of the Dirac operator, known as…
We give a specific method to solve with quadratic complexity the linear systems arising in known algorithms to deal with the sign determination problem. In particular, this enable us to improve the complexity bound for sign determination in…