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With the aim to solve the time-dependent Schr\"{o}dinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent $\mathcal{PT}$-symmetric one.…
We extend the derivation of the time-dependent Hartree-Fock equation recently obtained in [2] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the…
An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a fermion system trapped in a harmonic potential…
Theoretical approaches to the photoionization of few-electron atoms are discussed. These include nonequilibrium Greens functions and wave function based approaches. In particular, the Multiconfiguration Time-Dependent Hartree-Fock method is…
We analyze the solutions of the Schr\"odinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
Fully numerical mesh solutions of 2D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of atoms and…
A deterministic model with a large number of continuous and discrete degrees of freedom is described, and a statistical treatment is proposed. The model exactly obeys a Schrodinger equation, which has to be interpreted exactly according to…
We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix…
Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are even stronger restricted by so-called generalized Pauli constraints. Whenever given natural occupation numbers lie on the boundary of the allowed…
We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the…
Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schr\"odinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator…
We consider a system of N weakly interacting fermions with a real analytic pair interaction. We prove that for a general class of initial data there exists a fixed time T such that the difference between the one particle density matrix of…
We consider the Schr\"odinger equation with a (matrix) Hamiltonian given by a second order difference operator with nonconstant growing coefficients, on the half one dimensional lattice. This operator appeared first naturally in the…
We build an efficient and unitary (hence stable) method for the solution of the semi-classical Schr\"odinger equation subject with explicitly time-dependent potentials. The method is based on a combination of the Zassenhaus decomposition…
We consider the Fermi polaron problem at zero temperature, where a single impurity interacts with non-interacting host fermions. We approach the problem starting with a Frohlich-like Hamiltonian where the impurity is described with…
Based on previous works, analytical calculational procedures for dealing with the strongly interacting fermions ground state are further developed through a medium dependent potential in terms of the Bethe-Peierls contact interaction model.…
We study the dynamics of the thermal momentum distribution function for an interacting, homogenous Fermi gas on $\Z^3$ in the presence of an external weak static random potential, where the pair interactions between the fermions are modeled…