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Spontaneous symmetry breaking is examined by regarding it as a phenomenon in the eternal intermediate state due to sequential perturbations. The concept of the relativistic many-body state is applied to this intermediate state occurring in…

The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate…

An outstanding problem in the theory of nuclear fission is to understand the Hamiltonian dynamics at the scission point. In this work the fissioning nucleus is modeled in self-consistent mean-field theory as a set of Generator Coordinate…

We demonstrate and test the adiabatic projection method, a general new framework for calculating scattering and reactions on the lattice. The method is based upon calculating a low-energy effective theory for clusters which becomes exact in…

Sped-up protocols (shortcuts to adiabaticity) that drive a system quickly to the same populations than a slow adiabatic process may involve Hamiltonian terms difficult to realize in practice. We use the dynamical symmetry of the Hamiltonian…

We consider a reduced two-channel model of an atom consisting of a quantum dot coupled to an open scattering channel described by a three-dimensional Laplacian. We are interested in the survival probability of a bound state when the dot…

We extend a recent billiard model of the nuclear N-body Hamiltonian to consider a finite two-body interaction. This permits a treatment of the Hamiltonian by a mean field theory, and also allows the possibility to model reactions between…

The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an…

We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.

We introduce a class of non-Hermitian Hamiltonians that offers a dynamical approach to short-cut to adiabaticity (DASA). In particular, in our proposed 2 * 2 Hamiltonians, one eigenvalue is absolutely real and the other one is complex. This…

The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time…

In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between…

The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…

In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…

Diabatization of the molecular Hamiltonian is a standard approach to removing the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the…

The adiabatic approximation in quantum mechanics is considered in the case where the self-adjoint hamiltonian $H_0(t)$, satisfying the usual spectral gap assumption in this context, is perturbed by a term of the form $\epsilon H_1(t)$. Here…

We present numerical calculations, and simulations performed on a Rydberg atom quantum simulator, of the adiabatic evolution of many-body quantum systems around a quantum phase transition. We demonstrate that the end-to-end transfer error,…

Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an…

It is shown, that the Gamow-like model with only one adjustable parameter - radius constant is able to reproduce well the alpha-decay half-lives for all even-even nuclei with the proton number larger than 50. The systematics for odd-A and…

In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…