Algebraic time-reversal operation
نویسنده
چکیده
We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) ⊃ U(4) ⊃ K(4) = A(4) ∧ S(4) ⊃ S(4) ≈ Td. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators. PACS. 03.65.Fd Algebraic methods – 31.15.Hz Group theory
منابع مشابه
Quantum operation time reversal
The dynamics of an open quantum system can be described by a quantum operation: A linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal i...
متن کاملExpanded boundary integral method and chaotic time-reversal doublets in quantum billiards
We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal...
متن کاملStable algebraic spin liquid in a Hubbard model.
We show the existence of a stable algebraic spin liquid (ASL) phase in a Hubbard model defined on a honeycomb lattice with spin-dependent hopping that breaks time-reversal symmetry. The effective spin model is the Kitaev model for large on-site repulsion. The gaplessness of the emergent Majorana fermions is protected by the time-reversal invariance of this model. We prove that the effective spi...
متن کاملTime Reversal Invariance and Irreversibility 1. The standard approach to time reversal invariance for dynamical systems
1. The standard approach to time reversal invariance for dynamical systems State space . A process P is a parameterized curve s(t) in . So a process that describes the evolution from ti to tf is given by P : t 7! s(t); ti t tf . The reversaloperation is an involution R : s 7! Rs (Rs = s). Then the time reversed process is P : t 7! T s(t) := (Rs)( t); tf t ti. A theory is said to be time rever...
متن کاملPhotoacoustic image reconstruction of melanoma in skin tissue using time reversal method
This article has no abstract.
متن کامل