Related papers: Multi-scale methods in quantum field theory
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential…
The properties of a quantum dissipative scalar field is analyzed by Caldeira-Leggett model in strong-coupling regime. The Lagrangian of the total system is canonically quantized and the full Hamiltonian is diagonalized using Fano technique.…
Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and…
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…
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…
We use the discrete approach to solve the Schr\"odinger as well as the Bloch equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy…
We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function…
I revisit the ideas underlying dynamical decoupling methods within the framework of quantum information processing, and examine their potential for direct implementations in terms of encoded rather than physical degrees of freedom. The…
Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible due to the strong coupling…
Wavelet analysis is proposed as a new tool for studying the large-scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of one-dimensional cosmological density fluctuations is performed. In contrast…
We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
In these lecture notes, I review how to use large N techniques to solve quantum field theories in various dimensions. In particular, the case of N-dimensional quantum mechanics, non-relativistic cold and dense neutron matter, and scalar…
We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities,…
Quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of…
Blocking transformation is performed in quantum field theory at finite temperature. It is found that the manner temperature deforms the renormalized trajectories can be used to understand better the role played by the quantum fluctuations.…
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
Understanding dissipative and decohering processes is fundamental to the study of quantum systems. An accurate and generic method for investigating these processes is to simulate both the system and environment, which, however, is…