Quantum

About: Quantum is a research topic. Over the lifetime, 60044 publications have been published within this topic receiving 1233923 citations.

The quantum N-body problem and the auxiliary field method

Abstract: Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proven to be a powerful technique in the case of two-body problems. A general procedure is given and applied to various Hamiltonians of interest, in atomic and hadronic physics in particular. A test of formulas is performed for baryons described as a three-quark system.

Property (T) and exotic quantum group norms

Abstract: Utilizing the notion of property (T) we construct new examples of quantum group norms on the polynomial algebra of a compact quantum group, and provide criteria ensuring that these are not equal to neither the minimal nor the maximal norm. Along the way we generalize several classical operator algebraic characterizations of property (T) to the quantum group setting which unify recent approaches to property (T) for quantum groups with previous ones. The techniques developed furthermore provide tools to answer two open problems; firstly a question by B\'edos, Murphy and Tuset about automatic continuity of the comultiplication and secondly a problem left open by Woronowicz regarding the structure of elements whose coproduct is a finite sum of simple tensors.

The Complementarity of Quantum Observables: Theory and Experiments.

Abstract: Recent advances in experimental quantum physics have made it possible to perform joint measurements of complementary observables of individual quantum objects, like neutrons or photons. Despite its apparently contradictory nature, this statement is in full harmony with the quantum theory, the theory of complementarity [1], being, in fact, anticipated in the notion of coexistence. The concept of complementarity has both probabilistic and operational contents. When these two aspects are clearly distinguished, it becomes evident that probabilistically complementary observables may also be coexistent so that they can be measured together. This is exactly the situation encountered in recent experiments or in proposals for such experiments.

On the Singular Limit of the Quantum-Classical Molecular Dynamics Model

Abstract: In molecular dynamics applications there is a growing interest in so-called mixed quantum-classical models. These models describe most atoms of the molecular system by means of classical mechanics but describe an important, small portion of the system by means of quantum mechanics. A particularly extensively used model, the quantum-classical molecular dynamics (QCMD) model, consists of a singularly perturbed/ Schrodinger equation nonlinearly coupled to a classical Newtonian equation of motion.This paper studies the singular limit of the QCMD model for finite dimensional Hilbert spaces. The main result states that this limit is given by the time-dependent Born--Oppenheimer model of quantum theory---provided the Hamiltonian under consideration has a smooth spectral decomposition. This result is strongly related to the quantum adiabatic theorem. The proof uses the method of weak convergence by directly discussing the density matrix instead of the wave functions. This technique avoids the discussion of highly...