Abstract
The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ϵ-prescription where the non-uniform convergence of the limit ϵ → 0 leaves behind a spontaneous breakdown of the time reversal symmetry.
Highlights
One usually observes a system in interaction with its environment
The possible breakdown of the time reversal symmetry by the boundary conditions are detected by comparing two motions, one follows the real time evolution from the initial to the final boundary conditions and the initial and the final conditions are exchanged for the other. This makes the Closed Time Path (CTP) formalism, characterized by the redoubling of the degrees of freedom and evolving the doublers in opposite direction of the time, well suited to address this problem. This scheme is available both in the quantum and the classical level and has further important advantages, namely it provides a unique solution of the effective equation of motion with higher oder time derivatives, it allows the dynamical breakdown of the time reversal symmetry by treating the initial conditions as part of the dynamics and it supports dissipative forces which are local in time
The role of the environment initial conditions in generating soft irreversibility was studied in this work
Summary
One usually observes a system in interaction with its environment. The laws, discovered in such a manner are highly complex; they describe an open, effective rather than conserved, closed dynamics. This makes the Closed Time Path (CTP) formalism, characterized by the redoubling of the degrees of freedom and evolving the doublers in opposite direction of the time, well suited to address this problem This scheme is available both in the quantum and the classical level and has further important advantages, namely it provides a unique solution of the effective equation of motion with higher oder time derivatives, it allows the dynamical breakdown of the time reversal symmetry by treating the initial conditions as part of the dynamics and it supports dissipative forces which are local in time. Readers who like to be provided with a conceptual survey before being confronted with technical details are recommended to jump to Appendix A
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