相关论文: A Single Slice 2d Anderson Model at Weak Disorder

We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely, matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level…

The aim of these lectures is to describe a construction, as self-contained as possible, of renormalized gauge theories. Following a suggestion of Polchinski, we base our analysis on the Wilson renormalization group method. After a…

We consider the variance renormalisation of a singular SPDE for which a Da Prato-Debussche trick is not applicable. The example taken is the $2$-dimensional generalised parabolic Anderson model (gPAM), driven by a much rougher than white…

We present a Green's function technique for studying the nonlinear conductance of a nanocontact system with two electrodes at different chemical potentials. The retarded Green's function for a single-impurity Anderson model with two…

We consider a divergence-form elliptic difference operator on the lattice $\mathbb{Z}^d$, with a coefficient matrix that is an i.i.d. perturbation of the identity matrix. Recently, Bourgain introduced novel techniques from harmonic analysis…

The quantitative control of the dynamic correlations of single impurity Anderson models is essential in several very active fields. We analyze the one-particle Green function with a constant energy resolution by dynamic density-matrix…

Sequences of certain finite graphs, antitrees, are constructed along which the Anderson model shows GOE statistics, i.e. a re-scaled eigenvalue process converges to the ${\rm Sine}_1$ process. The Anderson model on the graph is a random…

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

We present a novel way of constructing reduced models for systems of ordinary differential equations. The reduced models we construct depend on coefficients which measure the importance of the different terms appearing in the model and need…

We implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos-Renyi random graphs, which represent an appropriate infinite dimensional limit. Our…

A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…

We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta \emph{et al.}…

Using the particular momentum conservation laws in dimension d=2, we can rewrite the Anderson model in terms of low momentum long range fields, at the price of introducing electron loops. The corresponding loops satisfy a Ward type…

We extend the two particle theory of disordered systems within the coherent potential approximation CPA to obtain weighted contributions to averaged two particle resolvents which arise from separate alloy components. Starting from first…

We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle…

We consider the problem of enumerating d-irreducible maps, i.e. planar maps whose all cycles have length at least d, and such that any cycle of length d is the boundary of a face of degree d. We develop two approaches in parallel: the…

The responsibility of a method/function is to perform some desired computations and disseminate the results to its caller through various deliverables, including object fields and variables in output instructions. Based on this definition…

We consider the periodic homogenisation problem for the generalised parabolic Anderson model on the two dimensional torus. We show that, for the renormalisation that respects Wick ordering, the homogenisation and renormalisation procedures…

We show how certain properties of the Anderson model on a tree are related to the solutions of a non-linear integral equation. Whether the wave function is extended or localized, for example, corresponds to whether or not the equation has a…

Transfer learning has remarkably improved computer vision. These advances also promise improvements in neuroimaging, where training set sizes are often small. However, various difficulties arise in directly applying models pretrained on…