We show that the computation of formation probabilities (FP) in the configuration basis and the full counting statistics (FCS) of observables in the quadratic fermionic Hamiltonians are equivalent to the calculation of emptiness formation probability (EFP) in the Hamiltonian with a defect. In particular, we first show that the FP of finding a particular configuration in the ground state is equivalent to the EFP of the ground state of the quadratic Hamiltonian with a defect. Then, we show that the probability of finding a particular value for any quadratic observable is equivalent to a FP problem and ultimately leads to the calculation of EFP in the ground state of a Hamiltonian with a defect. We provide new exact determinant formulas for the FP in the generic quadratic fermionic Hamiltonians. As applications of our formalism we study the statistics of the number of particles and kinks. Our conclusions can be extended also to the quantum spin chains that can be mapped to the free fermions via Jordan-Wigner (J-W) transformation. In particular, we provide an exact solution to the problem of the transverse field XY chain with a staggered line defect. We also study the distribution of magnetization and kinks in the transverse field XY chain and show how the dual nature of these quantities manifest itself in the distributions.
Impact of quantum coherence on the dynamics and thermodynamics of quenched free fermions coupled to a localized defect
Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；European Laboratory for Non-linear Spectroscopy（欧洲非线性光谱学实验室）；Università di Firenze（佛罗伦萨大学）；Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona（巴塞罗那自治大学物理系理论物理、信息与量子现象部门）；Centre for Quantum Materials and Technology, School of Mathematics and Physics, Queen’s University Belfast（贝尔法斯特女王大学数学与物理学院量子材料与技术中心）；Department of Physics, University of Trieste（的里雅斯特大学物理系）
Dynamics of number entropy for free fermionic systems in presence of defects and stochastic processes
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Indian Institute of Science Education and Research Pune（印度科学教育研究学院浦那分校）
Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
Sharif University of Technology（谢里夫理工大学）；Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究所）；Institute for Research in Fundamental Sciences (IPM)（基本科学研究院）
