Related papers: Loop Transfer Matrix and Loop Quantum Mechanics
We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…
We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…
The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by…
The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
Counting statistics of charge transfers in a point contact interacting with an arbitrary quantum system is studied. The theory for the charge specific density matrix is developed, allowing the evaluation of the probability of the outcome of…
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the…
A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of…
Transverse momentum dependent (TMD) distribution and fragmentation functions are described as Fourier transforms of matrix elementscontaining nonlocal combinations of quark and gluon fields. These matrix elements also contain a gauge link…
We consider the statistical mechanics of a class of models involving close-packed loops with fugacity $n$ on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite,…
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random…
We introduce a constructive procedure that maps all spatial correlations of a broad class of states into temporal correlations between general quantum measurements. This allows us to present temporal phenomena analogous to genuinely…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We introduce an algebraic Fourier transform for the quantum Toda lattice.
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
We show that the statistics of the charge transfer of non-interacting fermions through a two-lead contact is generalized binomial, at any temperature and for any form of the scattering matrix: an arbitrary charge-transfer process can be…
We consider quantum interferences of classically allowed or forbidden electronic trajectories in disordered dielectrics. Without assuming a directed path approximation, we represent a strongly disordered elastic scatterer by its…
Transfer matrices and matrix product operators play an ubiquitous role in the field of many body physics. This paper gives an ideosyncratic overview of applications, exact results and computational aspects of diagonalizing transfer matrices…