Related papers: The dual Burnside process
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
We study a Markov chain with very different mixing rates depending on how mixing is measured. The chain is the "Burnside process on the hypercube $C_2^n$." Started at the all-zeros state, it mixes in a bounded number of steps, no matter how…
We study the spectral properties of classical and quantum Markovian processes that are reset at random times to a specific configuration or state with a reset rate that is independent of the current state of the system. We demonstrate that…
The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which…
The permutation model is a classical spin system where elements of the symmetric group interact with one another. The partition function of this model is directly related to the entanglement structure of random quantum circuits and random…
The "quantum duality principle" states that the quantization of a Lie bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a quantization of the dual Lie bialgebra (through its associated formal Poisson group) - via…
In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…
We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is $k$, the resulting model is a continuous-time Markov chain on $k$ states and, as a consequence of the product…
A new operator based condition for distinguishing classical from non-classical states of quantised radiation is developed. It exploits the fact that the normal ordering rule of correspondence to go from classical to quantum dynamical…
Let R be a 1-dimensional integral domain, let h (non-zero) be a prime element, and let \HA be the category of torsionless Hopf algebras over R. We call H in \HA a "quantized function algebra" (=QFA), resp. "quantized restricted universal…
Dynamic fading channels are modeled at two fundamentally different levels of abstraction. At the physical layer, the standard representation is a correlated Gaussian process, such as the dB-domain signal power in log-normal shadow fading.…
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from…
Measurement-induced state disturbance is a major challenge in obtaining quantum statistics at multiple time points. We propose a method to extract dynamic information from a quantum system at intermediate time points, namely snapshotting…
We formalize the concept of subtime -- a reversible mode of information interchange within entangled systems -- and show how classical time emerges as an asymptotic limit through decoherence. Building on the photon clock model, in which a…
We present new theoretical results on the spectrum of the quantum field theory of the Double Sine Gordon model. This non-integrable model displays different varieties of kink excitations and bound states thereof. Their mass can be obtained…
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary…
Let R be an integral domain, let a non-zero h in R be such that k := R/hR is a field, and let HA be the category of torsionless (or flat) Hopf algebras over R. We call H in HA a "quantized function algebra" (=QFA), resp. "quantized…
We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…
In this work we study the stochastic process of two-species coagulation. This process consists in the aggregation dynamics taking place in a ring. Particles and clusters of particles are set in this ring and they can move either clockwise…
We analyse biased ensembles of trajectories for a two-dimensional system of particles, evolving by Langevin dynamics in a channel geometry. This bias controls the degree of particle clustering. On biasing to large clustering, we observe a…