相关论文: Interdimensional degeneracies for a quantum $N$-bo…

We show the existence of Borromean bound states in a one-dimensional quantum three-body system composed of two identical bosons and a distinguishable particle. It is assumed that there is no interaction between the two bosons, while the…

Symmetry implications for the decoherence of quantum oscillations of a two-state system in a solid are studied. When the oscillation frequency is small compared to the Debye frequency, the universal lower bound on the decoherence due to the…

A generalized contour deformation method (GCDM) which combines complex rotation and translation in momentum space, is discussed. GCDM gives accurate results for bound, virtual (antibound), resonant and scattering states starting with a…

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…

Considering coordinates as operators whose measured values are expectations between generalized coherent states based on the group SO(N,1) leads to coordinate noncommutativity together with full $N$ dimensional rotation invariance. Through…

Quantum entanglement manifests as a distinctive correlation between particles that transcends classical boundaries when their quantum states cannot be described independently. On the other hand, as quantum systems interact with their…

Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…

We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the…

This paper consists of two important theoretical observations on the interplay between l = 2 condensates; d-density wave (ddw), electronic nematic and d-wave superconducting states. (1) There is SO(4) invariance at a transition between the…

Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group D_l, where D_l is the group of order 2l generated by two rotations of angle…

We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…

We analyze planar $n$-body Hamiltonian systems with quadratic $D_n$-invariant interactions and identify the symmetry obstruction to choreographic motion. Choreographies are taken throughout to be collision-free solutions of the equations of…

Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic…

We derive explicit dimension formulas for irreducible $M_F$-spherical $K_F$-representations where $K_F$ is the maximal compact subgroup of the general linear group $GL(d,F)$ over a local field $F$ and $M_F$ is a closed subgroup of $K_F$…

Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbour interactions. We focus on the DE of a subsystem of L continuous spins. We show…

The quantum ground state properties of two independent chains of spins (two-levels systems) interacting with the same bosonic field are theoretically investigated. Each chain is coupled to a different quadrature of the field, leading to two…

This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…

The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions…