Related papers: Discretizing parametrized systems: the magic of Di…
We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main…
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
We discuss in detail the uniform discretization approach to the quantization of totally constrained theories. This approach allows to construct the continuum theory of interest as a well defined, controlled, limit of well behaved discrete…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We apply the ``consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and…
Lattice actions and amplitudes that perfectly mirror continuum physics are known as perfect discretizations. Such perfect discretizations naturally preserve the symmetries of the continuum. This is a key concern for general relativity,…
We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) non-periodic lattice close to a flat set in a lower dimensional space, typically a…
Understanding the continuum limit of a theory of discrete random geometries is a beautiful but difficult challenge. In this optic, we review here the insights that can be obtained for Causal Dynamical Triangulations (CDT) by employing the…
We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…
In this paper, we introduce a comprehensive axiomatization of structure-preserving discretization through the framework of commutative diagrams. By establishing a formal language that captures the essential properties of discretization…
Parameterized quantum circuits play a key role in quantum computing. Measuring the suitability of such a circuit for solving a class of problems is needed. One such promising measure is the expressivity of a circuit, which is defined in two…