Heat rectifiers are systems that conduct heat asymmetrically for forward and reversed temperature gradients. We present an analytical study of heat rectification in linear quantum systems. We demonstrate that asymmetric heat currents can be induced in a linear system only if it is dynamically driven. The rectification can be further enhanced, even achieving maximal performance, by detuning the oscillators of the driven network. Finally, we demonstrate the feasibility of such driven harmonic network to work as a thermal transistor, quantifying its efficiency through the dynamical amplification factor.Rectifiers are physical systems capable of conducting energy asymmetrically -whether electric, magnetic, thermal...-and are an essential building block in many technological applications. Although thermal rectifiers are crucial components to manipulate heat currents and construct phononic devices, so far no efficient and feasible thermal diodes have been found. Such device, when connected to two thermal baths at different temperatures, conducts heat asymmetrically if the temperatures of the baths are interchanged. This effect allows for an effective heat dissipation with a suppressed backflow reaction.To date, most theoretical proposals on classical heat rectifiers (see [1] and references therein) have been based either on the use of inohomogenous materials [2-7] exploiting nonlinear interactions, or doping the systems with impurities while remaining in the linear regime [8]. Also, the feasibility of microscopic systems acting as thermal devices has been recently addressed in, for instance, phononic refrigerators in the classical [9] and quantum [10] regimes, or heat rectifiers in diferent platforms: quantum dots [11], nonlinear solid-state quantum circuits [12], few-level systems [13,14], or hybrid configurations [15].Here, we address analytically and in full generality heat rectification in quantum systems under generic linear interactions. To this aim, we assume a network of harmonic oscillators coupled to two thermal reservoirs and investigate how asymmetric heat fluxes can be induced in such setup. First, we revisit the static scenario showing that linearity forbids heat rectification, regardless of any asymmetry in the harmonic network or in its coupling with the baths. Second, we demonstrate that heat rectification in a linear quantum system is possible if the system is periodically driven. This is our main result. Such feature is a consequence of two facts: (i) injecting/extracting work into/from a system by an external agent is a useful resource to redistribute energy and (ii) by periodically driven a system, new asymmetric heat transport processes -that have no analog in static scenarios-are induced. By using the Floquet formalism we identify precisely the quantum processes leading to heat rectification. Finally, we also demonstrate the suitability of driven harmonic net-works as heat transistors. Q r 1 FIG. 1. Sketch of a heat rectification setup where a system S with linear interactions V (t) is connected ...

Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not such a phase survives when systems are coupled to an environment. Although dissipation caused by the coupling to a bath may stabilize time crystals in some regimes, the introduction of incoherent noise may also destroy the time crystalline order. Therefore, the mechanisms that stabilize a time crystal in open and closed systems are not necessarily the same. Here, we propose a way to identify an open system time crystal based on a single object: the Floquet propagator. Armed with such a description we show time-crystalline behavior in an explicitly short-range interacting open system and demonstrate the crucial role of the nature of the decay processes.

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We study the storage capacity of quantum neural networks (QNNs), described by completely positive trace preserving (CPTP) maps acting on an N-dimensional Hilbert space. We demonstrate that attractor QNNs can store in a non-trivial manner up to N linearly independent pure states. For n qubits, QNNs can reach an exponential storage capacity, O ( 2 n ) , clearly outperforming standard classical neural networks whose storage capacity scales linearly with the number of neurons n. We estimate, employing the Gardner program, the relative volume of CPTP maps with M ⩽ N stationary states and show that this volume decreases exponentially with M and shrinks to zero for M ⩾ N + 1. We generalize our results to QNNs storing mixed states as well as input–output relations for feed-forward QNNs. Our approach opens the path to relate storage properties of QNNs to the quantum features of the input–output states. This paper is dedicated to the memory of Peter Wittek.

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