Exactly Solvable Inhomogeneous Fermion Systems
Copyright policy )Exactly Solvable Inhomogeneous Fermion Systems
Abstract 15 exactly solvable inhomogeneous (spinless) fermion systems on 1D lattices are constructed explicitly based on the discrete orthogonal polynomials of the Askey scheme, e.g. Krawtchouk, Hahn, Racah, Meixner, and q-Racah polynomials. The Schrödinger and Heisenberg equations are solved explicitly, as the entire set of the eigenvalues and eigenstates are known explicitly. The ground-state two-point correlation functions are derived explicitly. The multipoint correlation functions are obtained by Wick’s theorem. 15 corresponding exactly solvable XX spin systems are also displayed. They all have nearest-neighbor interactions. The exact solvability of the Schrödinger equation means that the corresponding Fokker–Planck equation is also exactly solvable. This leads to 15 exactly solvable birth and death fermions and 15 birth and death spin models. These provide plenty of material for calculating interesting quantities, e.g. entanglement entropy, etc.
High Energy Physics - Theory, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), FOS: Physical sciences, Schrödinger equation, Exactly and quasi-solvable systems arising in quantum theory, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), fermion systems, Racah polynomials, Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices, Heisenberg equation, Condensed Matter - Statistical Mechanics, Selfadjoint operator theory in quantum theory, including spectral analysis, \(q\)-Racah polynomials, Special quantum systems, such as solvable systems, Meixner polynomials, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), 1D lattices, Hahn polynomials, Fermionic systems in quantum theory, Applications of hypergeometric functions, High Energy Physics - Theory (hep-th), Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Krawtchouk polynomials, Quantum Physics (quant-ph)
High Energy Physics - Theory, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), FOS: Physical sciences, Schrödinger equation, Exactly and quasi-solvable systems arising in quantum theory, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), fermion systems, Racah polynomials, Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices, Heisenberg equation, Condensed Matter - Statistical Mechanics, Selfadjoint operator theory in quantum theory, including spectral analysis, \(q\)-Racah polynomials, Special quantum systems, such as solvable systems, Meixner polynomials, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), 1D lattices, Hahn polynomials, Fermionic systems in quantum theory, Applications of hypergeometric functions, High Energy Physics - Theory (hep-th), Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Krawtchouk polynomials, Quantum Physics (quant-ph)
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