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## First passage problems in classical and quantum processes

### Benjamin Walter (Imperial College London)

Hybrid: onsite seminar + zoom.

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In the first part of my talk I discuss the problem of first-passage times of a certain class of non-Markovian “active thermal” processes [1,2]. These are one-dimensional stochastic processes that are driven by both an uncorrelated (thermal) noise as well as a self-correlated (“active”) noise. I present a field theoretic perturbation theory, valid in the low-activity regime, which systematically computes the corrections to the survival probability, and hence allows one to extract distributions of first-passage times, running maxima and mean range via some simple relations. I further give a brief outlook on current work regarding processes driven by fractional Gaussian noise.

In the second part of my talk, I present some preliminary findings of an ongoing research project [3] studying the first detection time [4] of a many body quantum system. The first detection time is the first time that a quantum system is observed to be in a predefined state under repeated projective measurements. We study N, possibly infinite, free fermions which are arranged adjacently on a linear lattice. Under periodical projective measurements, performed at a period of \tau, we study the statistics of the return probability F_k(\tau); the probability to find the system in its initial state for the first time at the k-th attempt of measurement. The statistics of F_k(\tau) depend non-trivially on \tau, and we provide some analytical estimates based on recently found results on the N-fermion return amplitude [5], which are compared to exact computations.

(Jointly with Andrea Gambassi, Gabriele Perfetto, Gunnar Pruessner and Guillaume Salbreux)

References

1 B. Walter, G. Pruessner, G. Salbreux, Phys. Rev. Res. 3, 013075 (2021)

2 B. Walter, G. Pruessner, G. Salbreux, Phys. Rev. Res., in print (2022)

3 B. Walter, G. Perfetto, A. Gambassi, In preparation

4 H. Friedman, D. A. Kessler, E. Barkai, Phys. Rev. E , 95, 032141 (2017)

5 P. L. Krapivsky, J. M. Luck, K Mallick, Journal of Statistical Mechanics: Theory and Experiment 2018, 023104 (2018)