Discrepancies between decoherence and the Loschmidt echo

¹  Departamento de Física and IFIBA, FCEyN, UBA - Pabellón 1 Ciudad Universitaria, C1428EGA Buenos Aires, Argentina
²  Departamento de Física, Lab. TANDAR, Comisión Nacional de Energía Atómica - Av. del Libertador 8250, 1429 Buenos Aires, Argentina

Corresponding author: garciama@tandar.cnea.gov.ar

Received: 6 January 2010
Accepted: 24 February 2010

Abstract

The Loschmidt echo and the purity are two quantities that can provide invaluable information about the evolution of a quantum system. While the Loschmidt echo characterizes instability and sensitivity to perturbations, purity measures the loss of coherence produced by an environment coupled to the system. For classically chaotic systems both quantities display a number of —supposedly universal— regimes that can lead to think of them as equivalent quantities. We study the decay of the Loschmidt echo and the purity for systems with finite-dimensional Hilbert space and present numerical evidence of some fundamental differences between them.