相关论文: On Symmetries in Analytic Input-Output Systems
We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green's function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal…
Classical Lie group theory provides a universal tool for calculating symmetry groups for systems of differential equations. However Lie's method is not as much effective in the case of integral or integro-differential equations as well as…
We describe an algebraic framework for studying the symmetry properties of integrable quantum systems on the half line. The approach is based on the introduction of boundary operators. It turns out that these operators both encode the…
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run…
Symmetry is an important inductive bias that can improve model robustness and generalization across many deep learning domains. In multi-agent settings, a priori known symmetries have been shown to address a fundamental coordination failure…
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time-reversibility over the phase space is equivalent to the…
Recent studies have pointed out the intrinsic dependence of figures of merit of thermodynamic relevance -- such as work, heat and entropy production -- on the amount of quantum coherences that is made available to a system. However, whether…
The global symmetry data of a $D$-dimensional absolute quantum field theory can sometimes be packaged in terms of a $(D+1)$-dimensional bulk system obtained by extending along an interval, with a relative QFT$_D$ at one end and suitable…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial…
Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an…
We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it…
We unveil the universal (model-independent) symmetry satisfied by Schwinger-Keldysh quantum field theories whenever they describe equilibrium dynamics. This is made possible by a generalization of the Schwinger-Keldysh path-integral…
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…
A natural geometry, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is used to study the symmetry properties of real-space renormalisation group (RG) flow. In the projective…
The degree of symmetry of a combinatorial object, such as a lattice path, is a measure of how symmetric the object is. It typically ranges from zero, if the object is completely asymmetric, to its size, if it is completely symmetric. We…
Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant…
This thesis deals with the phase space realization of asymptotic higher spin symmetries, in 4d asymptotically flat spacetimes. In the gravitational case for instance, these symmetries generalize the BMS algebra to include an infinite tower…
Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time-reversibility have so far been limited to microscopic models.…