Related papers: Many-fermion wave functions: structure and example…
In some special zones of the high-dimensional coordinate space of few-body systems with identical particles, the operation of an element (or a product of elements) of the symmetry groups of the Hamiltonian on a quantum state might be…
We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural, well-known…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
For finite quantum many-particle systems modeled with say $m$ fermions in $N$ single particle states and interacting with $k$-body interactions ($k \leq m$), the wavefunction structure is studied using random matrix theory. Hamiltonian for…
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
Orbital magnetism is a purely quantum phenomenon that reflects intrinsic electronic properties of solids, yet its microscopic description in interacting multiband systems remains incomplete. We develop a general quantum many-body framework…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems,…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
For different cohomology theories (including the Hochschild homology, Hodge cohomology, Chow groups, and Grothendieck groups of coherent sheaves), we identify the cohomology of moduli space of rank 1 perverse coherent sheaves on the blow-up…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation -- so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body…
Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description,…