The Special Theory of Relativity and Quantum Mechanics merge in the keyprinciple of Quantum Field Theory, the Principle of Locality. We review someexamples of its ``unreasonable effectiveness'' (which shows up best in theformulation of Quantum Field Theory in terms of

Let $\mu$ be the self-avoiding walk connective constant on $\ZZ^d$. We showthat the asymptotic expansion for $\beta_c=1/\mu$ in powers of $1/(2d)$satisfies Borel type bounds. This supports the conjecture that the expansion isBorel summable.

In this paper, we introduce and study unified $(r,s)$-relative entropy andquantum unified $(r,s)$-relative entropy, in particular, our main results ofquantum unified $(r,s)$-relative entropy are established on the separablecomplex Hilbert spaces. Moreover, the entanglement-measure of states due to thequantum unified $(r,s)$-relative

A new family of decagonal quasiperiodic tilings are constructed by the use ofgeneralized point substitution processes, which is a new substitution formalismdeveloped by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. Thesetilings are composed of three prototiles: an

The validity of the Ehrenfest's theorem in Abelian and non-Abelian quantumfield theories is examined. The gauge symmetries are taken to be unbroken. Bysuitably choosing the physical subspace, the above validity is proven in boththe cases.

We investigate the kinetics of a particle exerted by a constant externalforce on a Lie-algebraic noncommutative space. The structure constants of a Liealgebra, also called noncommutative parameters, are constrained in general dueto some algebraic properties, such as the antisymmetry and

This paper deals with multiphase models for the growth of tumor masses ininteraction with a surrounding tissue. Models specialize in nonlinear systemsof possibly degenerate parabolic equations, which contain phenomenologicalterms translating specific biological mechanisms and which require to besupplemented by biologically

We consider the defocussing NLS equation with small periodic initialcondition. A new approach to study the Hamiltonian as a function of actionvariables is demonstrated. The problems for the NLS equation is reformulated asthe problem of conformal mapping theory corresponding to

We investigate the relation between the symmetries of a quantum system andits topological quantum numbers, in a general C*-algebraic framework. We provethat, under suitable assumptions on the symmetry algebra, there exists ageneralization of the Bloch-Floquet transform which induces a direct-integraldecomposition

We describe the essential spectrum and prove the Mourre estimate for quantumparticle systems interacting through k-body forces and creation-annihilationprocesses which do not preserve the number of particles. For this we computethe ``Hamiltonian algebra'' of the system, i.e. the C*-algebra C

Symplectic invariants introduced in can be computed for anarbitrary spectral curve. For some examples of spectral curves, thoseinvariants can solve loop equations of matrix integrals, and many problems ofenumerative geometry like maps, partitions, Hurwitz numbers, intersectionnumbers, Gromov-Witten invariants... The problem

Random matrices are used in fields as different as the study ofmulti-orthogonal polynomials or the enumeration of discrete surfaces. Both ofthem are based on the study of a matrix integral. However, this term can beconfusing since the definition of a

We formulate and discuss a number of conjectures on the ground state vectorsof the XYZ-spin chains of odd length with periodic boundary conditions and aspecial choice of the Hamiltonian parameters. In particular, arguments for thevalidity of a sum rule for

Each H^k Sobolev inner product defines a Hamiltonian vector field X_k on theregular dual of the Lie algebra of the diffeomorphism group of the circle. Weshow that only X_0 and X_1 are bi-Hamiltonian relatively to a modifiedLie-Poisson structure.

Resultants are getting increasingly important in modern theoretical physics:they appear whenever one deals with non-linear (polynomial) equations, withnon-quadratic forms or with non-Gaussian integrals. Being a subject of morethan three-hundred-year research, resultants are of course rather well studied:a lot of explicit

We define a quasiclassical limit of the Lian-Zuckerman homotopy BV algebra(quasiclassical LZ algebra) on the subcomplex, corresponding to "light modes",i.e. the elements of zero conformal weight, of the semi-infinite (BRST)cohomology complex of the Virasoro algebra associated with vertex operatoralgebra (VOA)

We summarize the main ideas of General Relativity and Lorentzian geometry,leading to a proof of the simplest of the celebrated Hawking-Penrosesingularity theorems. The reader is assumed to be familiar with Riemanniangeometry and point set topology.

Stimulated Raman adiabatic passage (STIRAP) is a well established techniquefor producing coherent population transfer in a three-state quantum system. Wehere exploit the resemblance between the Schrodinger equation for such aquantum system and the Newton equation of motion for a classical

The pure Skyrme-Faddeev-Niemi model (i.e., without quadratic kinetic term)with a potential is considered on the spacetime S^3 x R. For one-vacuumpotentials two types of exact Hopf solitons are obtained. Depending on thevalue of the Hopf index, we find compact or