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The quantum-to-classical correspondence (QCC) in spin models is a puzzling phenomenon where the static susceptibility of a quantum system agrees with its classical-system counterpart, at a different corresponding temperature, within the…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
Transverse pattern formation in an optical cavity containing a cloud of cold two-level atoms is discussed. We show that density modulation becomes the dominant mechanism as the atomic temperature is reduced. Indeed, for low but achievable…
Measurement of a quantum system provides information concerning the state in which it was prepared. In this paper we show how the retrodictive formalism can be used to evaluate the probability associated with any one of a given set of…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
It is common knowledge that atoms can form molecules if they attract each other. Here, we show that it is possible to create molecules where bound states of the atoms are not the result of attractive interactions but have the topological…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
Exact two-dimensional analytic wave functions for an arbitrary number $N$ of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of…
We introduce a classical analog of quantum matter in ultracold molecule -- or Rydberg atom -- synthetic dimensions, extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying…
In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition which leads to an effective…
It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures,…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
The temporal evolution of quantum statistical properties of an interacting atom-radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. To…
Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix $\rho_1$, obtained by…
The interaction energy between two atoms is crucially dependent on the quantum state of the two-atom system. In this paper, it is demonstrated that a steady resonance interaction energy between two atoms exists when the atoms are in a…
A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…
The approximate representation of a quantum solid as an equivalent composite semi-classical solid is considered for insulating materials. The composite is comprised of point ions moving on a potential energy surface. In the classical bulk…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
The classical model that describes the motion of an atom in a magnetic trap is solved in order to investigate the relationship between the failure of the usual adiabatic approximation assumption and the physical parameters of the trap. This…
The dynamical evolution of a quantum system composed of two coupled cavities, each containing a two-level atom and a single-mode thermal field, is investigated under different conditions. The entanglement between the two atoms is controlled…