Related papers: Pattern formation in quantum Turing machines
We investigate Turing's notion of an A-type artificial neural network. We study a refinement of Turing's original idea, motivated by work of Teuscher, Bull, Preen and Copeland. Our A-types can process binary data by accepting and outputting…
We show that the dynamics resulting from preparing a one-dimensional quantum system in the ground state of two decoupled parts, then joined together and left to evolve unitarily with a translational invariant Hamiltonian (a local quench),…
We study post-quench dynamics of charge-density-wave (CDW) order in the square-lattice $t$-$V$ model. The ground state of this system at half-filling is characterized by a checkerboard modulation of particle density. A generalized…
Schlesinger transformations are discrete monodromy preserving symmetry transformations of a meromorphic connection which shift by integers the eigenvalues of its residues. We study Schlesinger transformations for twisted sl_N-valued…
We extend the orbital-dependent electron tunneling model implemented within the three-dimensional (3D) Wentzel-Kramers-Brillouin (WKB) atom-superposition approach for simulating scanning tunneling microscopy (STM) by including arbitrary tip…
We study the Schwinger effect, in which the external field having a spatiotemporal profile creates electron-positron pairs via multidimensional quantum tunneling. Our treatment is based on the trace formula for the QED effective action,…
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state…
Unitary evolutions of a qubit are traditionally represented geometrically as rotations of the Bloch sphere, but the composition of such evolutions is handled algebraically through matrix multiplication [of SU(2) or SO(3) matrices].…
It has been recently shown that in quantum systems, the complex time evolution typical of many-bodied coupled networks can be transformed into a simple, relaxation-like dynamics, by relying on periodic dephasings of the off-diagonal density…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive…
The manipulation of single spins through spin-polarized tunneling opens new routes for quantum control at the atomic scale. We present a theoretical framework describing spin-transfer, spin torques and spin resonance in molecular quantum…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…
We study the interplay between an inhomogeneous quantum quench of the external potential in a system of relativistic fermions in one dimension and the well-known Klein tunneling. We find that the large time evolution is characterized by…
It was recently shown that a generalization of quantum Turing machines (QTMs), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states…
The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…
Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to adjust over time proved cumbersome and led to conclusions…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
We study quantum quenches in the $S=1$ Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum…