منابع مشابه
Non-Hermitian matrix description of the PT −symmetric anharmonic oscillators
The PT −symmetric differential Schrödinger equation Hψ = Eψ with the operator H = H(x) = p + a x + i β x + c x + i δ x ≡ H∗(−x) on L2(−∞,∞) is studied. At a > 0 it is re-arranged as a linear algebraic diagonalization. With rigorous proof, our non-variational construction of bound states offers an infinite-dimensional analogue to the recent finite-dimensional quasi-exact solution available at th...
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We examine a new application of the Holstein-Primakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinite-dimensional representations of the Lie algebra su(2). The representations contain nonstandard raising and lowering operators, which are nonlinearly related to the standard a† and a. The new operators also give rise to a natural family of two-oscilla...
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We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the x and p appearing in the Hamiltonian, but quantities X and P constructed by means of the metric operator. Following the analogous procedure of gauging a global symmetry in Hermitian quantum mechanics we find t...
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Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal...
متن کاملAn Equivalent Hermitian Hamiltonian for the non-Hermitian −x4 Potential
The potential V (x) = −x4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT symmetric rather than Hermitian. Nonetheless it has been shown numerically to have a real spectrum, and a proof of reality, involving the correspondence between ordinary differential equations and inte...
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ژورنال
عنوان ژورنال: Annals of Physics
سال: 2015
ISSN: 0003-4916
DOI: 10.1016/j.aop.2014.11.018