Abstract
The Keldysh formalism is capable of describing driven-dissipative dynamics of open quantum systems as nonunitary effective field theories that are not necessarily thermodynamical, thus often exhibiting new physics. Here, we introduce a general Keldysh action that maximally obeys Weinbergian constraints, including locality, Poincar\'e invariance, and two "$CPT$" constraints: complete positivity and trace preserving as well as charge, parity, and time reversal symmetry. We find that the perturbative Lindblad term responsible for driven-dissipative dynamics introduced therein has the natural form of a double-trace deformation $\mathcal{O}^2$, which, in the large $N$ limit, possibly leads to a new nonthermal conformal fixed point. This fixed point is IR when $\Delta<d/2$ or UV when $\Delta>d/2$ given $d$ the dimensions of spacetime and $\Delta$ the scaling dimension of $\mathcal{O}$. Such a UV fixed point being not forbidden by Weinbergian constraints may suggest its existence and even completion of itself, in contrast to the common sense that dissipation effects are always IR relevant. This observation implies that driven-dissipative dynamics is much richer than thermodynamics, differing in not only its noncompliance with thermodynamic symmetry (e.g., the fluctuation-dissipation relation) but its UV/IR relevance as well. Examples including a $(0+1)$-$d$ harmonic oscillator under continuous measurement and a $(4-\epsilon)$-$d$ classic $O(N)$ vector model with quartic interactions are studied.
Highlights
Quantum mechanics, despite its extreme success in predicting and agreeing with every experimental outcome, still bemuses everyone by “suspiciously” postulating the existence of two distinct but necessary time-evolution mechanisms, i.e., reversible unitary dynamics versus irreversible wave function collapse [1]
The main result we find for our Keldysh action is that, under appropriately renormalized perturbation, the nonunitary terms responsible for driven-dissipative dynamics have the natural form of a double-trace deformation [32,33,34,35] which has been very thoroughly studied—especially in the literature of conformal field theory (CFT) [36,37]
UV CFTs connected by a double-trace deformation O⊺O of large N have a natural explanation in the bulk AdS space: the only difference between them amounts to a change of the boundary conditions [65] to the bulk equations of motion (EOM) near z → 0 in the Poincarepatch, ds2
Summary
Despite its extreme success in predicting and agreeing with every experimental outcome, still bemuses everyone by “suspiciously” postulating the existence of two distinct but necessary time-evolution mechanisms, i.e., reversible unitary dynamics versus irreversible wave function collapse [1]. Tracing out the environment’s d.o.f. is carried out by the use of the Feynman-Vernon influential functional [26], leaving an effective field theory (EFT) as a Keldysh pathintegral functional where only the bra and ket fields corresponding to the remaining d.o.f. are kept This promising method of describing many-body OQS in a field-theoretical language has been actively discussed both in the nonrelativistic context [16] and relativistic context [24,25] and has led to new research directions such as novel universality class in quantum phase transition [27], information loss in EFT [28,29], etc. This may lead to a refreshing perspective of how a Keldysh CFT living on the boundary corresponds to the bulk theory, which we will briefly discuss at the end
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