## Adapted Caldeira-Leggett

These papers have been posted in May2021. Contextual updates to these pages reflecting the new work are expected to be completed in summer 2021.

arXiv:2105.14017 **Einselection, Equilibrium and Cosmology**

Abstract: Our observed Universe has a very strong arrow of time rooted in its low entropy starting point. This low entropy start can be related to various "tuning puzzles" about the early state of the Universe. Here we explore the relationship between the arrow of time and the emergence of classical from quantum in the hopes of ultimately gaining insights into cosmological initial conditions. Our focus is o… ▽ More

arXiv:2105.14040 **Adapted Caldeira-Leggett Model**

Abstract: We preset a variant of the Caldeira-Leggett (CL) model of a harmonic oscillator coupled to an environment. The CL model is a standard tool for studying the physics of decoherence. Our "adapted Caldeira-Leggett" (ACL) model is built in a finite Hilbert space which makes it suitable for numerical studies. Taking a numerical approach allows us to avoid the limitations of standard approximation scheme… ▽ More

arXiv:2105.14032 **Copycat process in the early stages of einselection**

Abstract: We identify and describe unique early time behavior of a quantum system initially in a superposition, interacting with its environment. This behavior -- the copycat process -- occurs after the system begins to decohere, but before complete einselection. To illustrate this behavior analytic solutions for the system density matrix, its eigenvalues, and eigenstates a short time after system-environme… ▽ More

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Andrew Arrasmith and I have developed an "Adapted Caldeira-Leggett" (ACL) model. Like the original Caldeira-Leggett (CL) model it is useful for exploring the quantum aspects of a system interacting with an environment. Unlike the CL model, the ACL occupies a finite Hilbert space and is amenable to numerical calculations. We have performed various numerical explorations which in the first instance show decoherence and einselection phenomena similar to those seen with the CL model. Our next exploration has been to study these phenomena under equilibrium conditions, where there is no arrow of time. This is a very different regime vs the usual CL studies, which use master equation techniques that presuppose an arrow of time throughout. As of April 2019 publications on these topics are in preparation. Here are some of my recent talks on the subject.

- April 4, 2019 University of Nottingham Seminar (Slides here)
- See also the Copenhagen talks on this page from April 2018 (under "Reviews of cosmic inflation"). The work was not as full developed then, but those talks give more of the motivations and background.
- Also, for general background information on decoherence and einselection, here are some excellent review articles by Zurek and by Schlosshauer.

The **"copycat state"**: We observe an interesting two step process toward einselection. If one starts with an initial "Schrödinger Cat" superposition of wavepackets, the first step involves the density matrix acquiring a 2nd (small) nonzero eigenvalue with a corresponding eigenstate that has a "copycat" form. This 2nd eigenstate looks something like a mirror image of the original Schrödinger cat state. It remains stable for a while, and then on the full decoherence time the two eigenstates "collapse" into the single wavepacket (pointer basis) form. These slides illustrate the whole process.