9 papers
Unitary -designs without independent Hamiltonian quenches
Pratik Nandy
Unitary -designs provide a resource-efficient framework for emulating Haar randomness up to the -th order. Quench-based protocols have recently been shown to generate such de…
Krylov Complexity Under Hamiltonian Deformations and Toda Flows
Kazutaka Takahashi, Pratik Nandy, Adolfo del Campo
The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for H…
Complexity of Quadratic Quantum Chaos
Pallab Basu, Suman Das, Pratik Nandy
We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum cha…
Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
Viktor Jahnke, Pratik Nandy, Kuntal Pal +2
Utilizing the framework of free probability, we analyze the spectral and operator statistics of the Rosenzweig-Porter random matrix ensembles, which exhibit a rich phase structure…
Quantum Dynamics in Krylov Space: Methods and Applications
Pratik Nandy, Apollonas S. Matsoukas-Roubeas, Pablo MartÃnez-Azcona +2
The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods t…
Krylov space approach to Singular Value Decomposition in non-Hermitian systems
Pratik Nandy, Tanay Pathak, Zhuo-Yu Xian +1
We propose a tridiagonalization approach for non-Hermitian random matrices and Hamiltonians using singular value decomposition (SVD). This technique leverages the real and non-nega…