Related papers: The K-sat problem in a simple limit
By considering the enlarged thermal system including the heat bath, it is shown that this system has supersymmetry which is not broken at finite temperature. The super algebra is constructed and the Hamiltonian is expressed as the…
The paper [1] considers a spherical cloak described by three radially varying acoustical quantities. For a given radial mass density in the cloak the question posed is whether the remaining two parameters, tangential density and…
We study the set of solutions of random k-satisfiability formulae through the cavity method. It is known that, for an interval of the clause-to-variables ratio, this decomposes into an exponential number of pure states (clusters). We refine…
In this work, by investigating the low temperature behaviour of a scalar field around a cosmic string, and assuming stable thermodynamic equilibrium, it is shown that the coupling parameter of the field with curvature must be restricted to…
We construct a class of one-dimensional Lie-algebraic problems based on sl(2) where the spectrum in the algebraic sector has a dynamical symmetry E -> - E. All 2j+1 eigenfunctions in the algebraic sector are paired, and inside each pair are…
We discuss a recent approach for overcoming the poor convergence of the perturbative expansion for the thermodynamic potential of QCD. This approach is based on self-consistent approximations which allow for a gauge-invariant and manifestly…
We consider the Cooper-problem on a lattice model including onsite and near-neighbor interactions. Expanding the interaction in basis functions for the irreducible representation for the point group $C_{4v}$ yields a classification of the…
It is shown how quantum field theory at finite temperature can be used to set up self-consistent and gauge invariant equations for cosmological perturbations sustained by an ultrarelativistic plasma. While in the collisionless case, the…
An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q^{({\rm RS})}_{ab} = \delta_{ab} + q(1-\delta_{ab})$ is investigated. In particular, when the expansion is…
The analytic properties in the energy variable k_{0} of finite-temperature self-energies are investigated. A typical branch cut results from n particles being emitted into the heat bath and n' being absorbed from the heat bath. There are…
The third law of thermodynamics forbids cooling a physical system to absolute zero in a finite number of operational steps. Although this unattainability principle has been quantified for specific state-to-state transitions, a universal,…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
An algebraic framework for quantization in presence of arbitrary number of point-like defects on the line is developed. We consider a scalar field which interacts with the defects and freely propagates away of them. As an application we…
Quantum k-SAT (the problem of determining whether a k-local Hamiltonian is frustration-free) is known to be QMA_1-complete for k >= 3, and hence likely hard for quantum computers to solve. Building on a classical result of Alon and Shapira,…
Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the…
The CNF formula satisfiability problem (CNF-SAT) has been reduced to many fundamental problems in P to prove tight lower bounds under the Strong Exponential Time Hypothesis (SETH). Recently, the works of Abboud, Hansen, Vassilevska W. and…
We report the continuum limits of the speed of sound, c_s, and the specific heat at constant volume, c_v, in quenched QCD at temperatures of 2Tc and 3Tc. At these temperatures, c_s is within 2-sigma of the ideal gas value, whereas c_v…
Several fragments of the satisfiability problem have been studied in the literature. Among these, Linear 3-SAT is a satisfaction problem in which each clause (viewed as a set of literals) intersects with at most one other clause; moreover,…
Quantum thermodynamics with open systems is often based on the quantum optical weak-coupling master equation or on operational repeated interaction models, whereas early works on thermalisation and on decoherence theory were mostly…
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant challenge at the confluence of physics and mathematics. This…