## Decoherence in a box

### New Directions in the Foundations of Physics 2014

Schrodinger considered superposition the characteristic
trait of quantum mechanics:

"

*When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that***but rather**__one__**characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives [the quantum states] have become entangled.”**__the__
So why we don’t see then in our macroscopic world a cat both
dead

**and**alive? In other words, how does classicality emerge from quantum mechanics? The answer comes (in part) from decoherence which shows that interaction with environment makes the density matrix diagonal, free of interference terms. But is this a general enough mechanism?
In his talk “A Closed System Perspective for Decoherence”, Sebastian
Fortin presented a framework which generalizes the current approach

**systems.**__for both open and closed__
First let’s present the problem with closed systems. Unitary
time evolution in quantum mechanics can prevent canceling the non-diagonal
parts of the density matrix in a closed system. Decoherence works for open systems
by talking advantage of the very large numbers of degrees of freedom of the
environment which can absorb the “unwanted” information. There are two time characteristics
in an open quantum system: decoherence time and relaxation time. You can have decoherence without equilibrium (an
obvious example are the planets of the solar system) but dissipation always
implies decoherence. (This means that a quantum system reaches decoherence faster
than equilibrium.)

But how can we talk about irreversible processes in quantum
mechanics? Doesn’t this contradict unitary time evolution? Non-unitary time
evolution can arise when we sum over (trace over) the degrees of freedom of the
environment. This leads to a (non-unitary)

**master equation**.
In a

**, equilibrium or standard decoherence may not occur, but we can still get emergent classical behavior. So here is Fortin’s proposed solution: non-unitary time evolution is achieved by**__closed systems__**:**__course-graining__- split the information in relevant and irrelevant parts
- compute time evolution of relevant observables
- determine if you reach equilibrium (achieve relaxation)
- if so, compute the decay times

This is not at all unusual: for example in the kinetic
theory of gasses individual molecules never rest and reach (static) equilibrium. However,
course graining can extract the relevant macroscopic information: gas density,
pressure, etc.

In a closed quantum system

__the non-diagonal elements do not go to zero, but they may cancel each other out.__
This mechanism also works in open systems in addition to the
standard way of evolving the non-diagonal elements to zero. Hence, the
framework is universal. As an application: Fortin talked about self-induced
decoherence:

- Operators
belong to
*relevant observables**O* - States
belong to dual of
*O* - Computed expectation values are real quantities

A good example of relevant observables is van Hove
observables. To understand more of the proposed framework, I recommend this
paper: “The problem of identifying the system and the environment in the phenomenon of decoherence”.

The key strength of the proposed unified classicality emergence framework
is that it can be put to the test against real physical systems, and its predictions
can be confirmed or not by experiments.

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