Coarse grained quantum dynamics

Abstract

Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short-distance and long-distance degrees of freedom (d.o.f.), coupled via the Hamiltonian. Observations using purely long-distance observables are described by the reduced density matrix that arises from tracing out the short-distance d.o.f. The dynamics of this density matrix is non-Hamiltonian and nonlocal in time, on the order of some short time scale. We describe this dynamics in a model system with a simple hierarchy of energy gaps ΔE UV > ΔE IR , in which the coupling between high-and low-energy d.o.f. is treated to second order in perturbation theory. We then describe the equations of motion under suitable time averaging, reflecting the limited time resolution of actual experiments, and find an expansion of the master equation in powers of ΔE IR =ΔE UV , after the fashion of effective field theory. The failure of the system to be Hamiltonian or even Markovian appears at higher orders in this ratio. We compute the evolution of the density matrix in three specific examples: coupled spins, linearly coupled simple harmonic oscillators, and an interacting scalar quantum field theory. Finally, we argue that the logarithm of the Feynman-Vernon influence functional is the correct analog of the Wilsonian effective action for this problem.

Hot accelerated qubits: decoherence, thermalization, secular growth and reliable late-time predictions

“…for all t. This differential relation is sufficient to justify (1.2), and perturbation theory is then simply used to derive the value of the coefficient Γ. An argument similar in spirit to this -though different in detail -is also often available for computing the late-time limit of open systems [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. We argue here that for many OpenEFT applications it is the Lindblad equation [41,42] that is the desired evolution equation for these purposes.…”

Hot cosmic qubits: late-time de Sitter evolution and critical slowing down

“…where I and I are identity operators. 3 The total Hamiltonian is H = H 0 + H int 0 where the qubit/field coupling is described by the interaction Hamiltonian 12) and the dimensionless coupling 0 < g 1 is small enough to justify a perturbative treatment. We follow common convention and choose m = σ 1 , but all that really counts is that m and h do not commute with one another so that H int 0 drives transitions between the zeroeth-order qubit energy eigenstates.…”

“…A short calculation reveals that I 11 (τ ) = 11 (τ ) and I 12 (τ ) = e +iωτ 12 (τ ). This means that the diagonal solution (3.16) is unchanged in the interaction-picture, while the off-diagonal solution is I 12 (τ ) 12 (0)e −τ /ξ M + * 12 (0)…”

“…Similarities between the physics of quantum systems in gravitational spacetimes (especially with horizons) and open systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] show that this assumption is actually unlikely to be true. The problem is that open systems (by definition) always have an 'environment' whose properties are not measured (in this case, perhaps, the degrees of freedom behind the horizon).…”

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

“…We here follow [48] (see also [49,50]) and identify the relevant long-wavelength EFT for cosmology using the language of open systems, a research area started with [51] (see also [52] for a review on applications to cosmology). Because super-Hubble modes move through an environment of sub-Hubble modes with which information is exchanged (such as when modes pass from sub-to super-Hubble at horizon exit) they form an open system.…”