اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSupersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
56
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=omega J_{3}+alpha J_{-}+beta J_{+}$, $alpha eq beta$, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.
قيم البحث
اقرأ أيضاً
Distant boundaries in linear non-Hermitian lattices can dramatically change energy eigenvalues and corresponding eigenstates in a nonlocal way. This effect is known as non-Hermitian skin effect (NHSE). Combining non-Hermitian skin effect with nonline
ar effects can give rise to a host of novel phenomenas, which may be used for nonlinear structure designs. Here we study nonlinear non-Hermitian skin effect and explore nonlocal and substantial effects of edges on stationary nonlinear solutions. We show that fractal and continuum bands arise in a long lattice governed by a nonreciprocal discrete nonlinear Schrodinger equation. We show that stationary solutions are localized at the edge in the continuum band. We consider a non-Hermitian Ablowitz-Ladik model and show that nonlinear exceptional point disappears if the lattice is infinitely long.
Information on quantum systems can be obtained only when they are open (or opened) in relation to a certain environment. As a matter of fact, realistic open quantum systems appear in very different shape. We sketch the theoretical description of open
quantum systems by means of a projection operator formalism elaborated many years ago, and applied by now to the description of different open quantum systems. The Hamiltonian describing the open quantum system is non-Hermitian. Most studied are the eigenvalues of the non-Hermitian Hamiltonian of many-particle systems embedded in one environment. We point to the unsolved problems of this method when applied to the description of realistic many-body systems. We then underline the role played by the eigenfunctions of the non-Hermitian Hamiltonian. Very interesting results originate from the fluctuations of the eigenfunctions in systems with gain and loss of excitons. They occur with an efficiency of nearly 100%. An example is the photosynthesis.
Generalized coherent states are developed for SU(n) systems for arbitrary $n$. This is done by first iteratively determining explicit representations for the SU(n) coherent states, and then determining parametric representations useful for applicatio
ns. For SU(n), the set of coherent states is isomorphic to a coset space $SU(n)/SU(n-1)$, and thus shows the geometrical structure of the coset space. These results provide a convenient $(2n - 1)$--dimensional space for the description of arbitrary SU(n) systems. We further obtain the metric and measure on the coset space, and show some properties of the SU(n) coherent states.
Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one by a Hermit
ian similarity transformation. We extend the concept of non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. At zero temperature the PT phase transition is identified as the point at which the solutions cease to be real. Surprisingly for solutions containing black holes real solutions can be found well outside the quasi-Hermitian regime. These backgrounds are however unstable to fluctuations which establishes the persistence of the holographic dual of the PT phase transition at finite temperature.
The hallmark of symmetry-protected topological (SPT) phases is the existence of anomalous boundary states, which can only be realized with the corresponding bulk system. In this work, we show that for every Hermitian anomalous boundary mode of the te
n Altland-Zirnbauer classes, a non-Hermitian counterpart can be constructed, whose long time dynamics provides a realization of the anomalous boundary state. We prove that the non-Hermitian counterpart is characterized by a point-gap topological invariant, and furthermore, that the invariant exactly matches that of the corresponding Hermitian anomalous boundary mode. We thus establish a correspondence between the topological classifications of $(d+1)$-dimensional gapped Hermitian systems and $d$-dimensional point-gapped non-Hermitian systems. We illustrate this general result with a number of examples in different dimensions. This work provides a new perspective on point-gap topological invariants in non-Hermitian systems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
