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With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
We study a quantum model with non-isotropic two-dimensional oscillator potential but with additional quadratic interaction $x_1x_2$ with imaginary coupling constant. It is shown, that for a specific connection between coupling constant and…
We study entanglement in a system of three coupled quantum harmonic oscillators. Specifically, we use the Schmidt decomposition to analyze how the entanglement is distributed among the three subsystems. The Schmidt decomposition is a…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the…
We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a…
We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of $N$ coupled Pais-Uhlenbeck oscillators of…
We investigated the locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in the coupling…
We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A {\bf 77}, 062516 (2008)] to evaluate the ground state static electric dipole polarizabilities (\alpha s) of several atomic…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
The bi-partite Gaussian state, corresponding to an anisotropic harmonic oscillator in a noncommutative-space, is investigated with the help of the Simon's separability condition (generalized Peres-Horodecki criterion). It turns out that, in…
This paper focuses on the geometric phase of entangled states of bi-partite systems under bi-local unitary evolution. We investigate the relation between the geometric phase of the system and those of the subsystems. It is shown that (1)…
We study two a priori unrelated constructions: the spectrum of edge modes in a band topological insulator or superconductor with a physical edge, and the ground state entanglement spectrum in an extended system where an edge is simulated by…
A method to treat the ground state correlations beyond the RPA is presented. A set of nonlinear equations taking into account effects of the ground state correlations on the pairing and phonon-phonon coupling is derived. The influence of…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both…
Bosonic two-ring ladders constitute an important class of atomtronic circuits, where coherent current flows not only can offer a new insight into many-body physics, but also can play the role of actual degrees of freedom, and hence allow…
We investigate the global basin structure of twisted states in nearest-neighbor coupled phase oscillators with a common phase shift $\alpha$. As $\alpha$ increases, basin boundaries become progressively more complex, with their fractal…
We consider a spinless particle coupled to a photon field and prove that even if the Schr\"odinger operator $p^2 + V$ does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz…