Related papers: Exact Renormalization Scheme for Quantum Anosov Ma…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
For $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter it is demonstrated that there is a class of renormalization schemes, in which the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) formula for the renormalization…
We present a detailed description of the recently proposed numerical renormalization group method for models of quantum impurities coupled to a bosonic bath. Specifically, the method is applied to the spin-boson model, both in the Ohmic and…
We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff $\Lambda$ (implemented through an exponential damping…
A renormalization scheme is suggested where QCD input parameters - quark mass and coupling constant - are expressed in terms of gauge invariant and infrared stable quantities. For the renormalization of coupling constant the quark anomalous…
The concept of adjusted sublevel set for a quasiconvex function was introduced in \cite{AuHa05} and the local existence of a norm-to-weak$^*$ upper semicontinuous base-valued submap of the normal operator associated to the adjusted sublevel…
The cubic regularization (CR) algorithm has attracted a lot of attentions in the literature in recent years. We propose a new reformulation of the cubic regularization subproblem. The reformulation is an unconstrained convex problem that…
We consider the quantized hyperbolic automorphisms on the 2-dimensional torus (or generalized quantum cat maps), and study the localization properties of their eigenstates in phase space, in the semiclassical limit. We prove that if the…
We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models, in which the Hamiltonian is gradually simplified along a parallel…
We propose a hybrid quantum approach to threshold and binarize a grayscale image through unsharp measurements (UM) relying on image histogram. Generally, the histograms are characterized by multiple overlapping normal distributions…
The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…
This paper develops a conformal renormalization scheme for compact sets $K \subset \mathbb{C}$. As one application of the conformal renormalization scheme we prove that for every isolated non-trivial connected component $E \subset K$ there…
Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle's state as it approaches the origin when the attractive coupling parameter is…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
Faure and Tsujii recently proposed a new quantization theory for symplectic Anosov diffeomorphisms. It combines prequantization with the study of the Pollicott--Ruelle resonances of an associated transfer operator. We apply this framework…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
We develop a renormalization method for calculating the electronic structure of single and double quantum dots under intense ac fields. The nanostructures are emulated by lattice models with a clear continuum limit of the effective-mass and…
We calculate the one-loop quantum corrections to the mass and central charge of N=2 and N=4 supersymmetric monopoles in 3+1 dimensions. The corrections to the N=2 central charge are finite and due to an anomaly in the conformal central…
A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in…
Explicit, exact periodic orbit expansions for individual eigenvalues exist for a subclass of quantum networks called regular quantum graphs. We prove that all linear chain graphs have a regular regime.