{"id":{"repo_id":"milano","oai_identifier":"oai:air.unimi.it:2434/1119575"},"canonical_url":"https://search.dev.ndltd.org/etd/milano/oai:air.unimi.it:2434/1119575","repository":{"repo_id":"milano","name":"Università degli Studi di Milano","base_url":"https://air.unimi.it/oai/request"},"display":{"title":"COMBINING QUANTUM TRAJECTORIES AND TIME-DEPENDENT VARIATIONAL MONTE CARLO FOR MANY-BODY OPEN QUANTUM SYSTEMS","abstract":"Simulating quantum systems is complex due to the “curse of dimensionality”, which is exacerbated in open quantum systems that interact with their environment. Indeed, tra- ditional computational methods struggle with the exponential growth of Hilbert space in these systems. This thesis introduces the Open-Time Variational Monte Carlo (otVMC) method, which combines the quantum trajectory formalism with Monte Carlo tech- niques to enable real-time simulations of open quantum systems. By exploiting stochas- tic Schrödinger equations and a variational approach, otVMC significantly reduces com- putational complexity. Applied to a dissipative many-body spin system with long-range interactions, this method successfully simulates up to 180 spins and provides insights into time evolution of the spin-squeezing parameter. Despite some limitations, such as potential biases and challenges with accuracy in the long-time evolution, otVMC offers a robust tool for studying the dynamics of large, strongly interacting systems and holds promise for future extensions to continuous and higher-dimensional systems.","abstract_html":"Simulating quantum systems is complex due to the “curse of dimensionality”, which is exacerbated in open quantum systems that interact with their environment. Indeed, tra- ditional computational methods struggle with the exponential growth of Hilbert space in these systems. This thesis introduces the Open-Time Variational Monte Carlo (otVMC) method, which combines the quantum trajectory formalism with Monte Carlo tech- niques to enable real-time simulations of open quantum systems. By exploiting stochas- tic Schrödinger equations and a variational approach, otVMC significantly reduces com- putational complexity. Applied to a dissipative many-body spin system with long-range interactions, this method successfully simulates up to 180 spins and provides insights into time evolution of the spin-squeezing parameter. Despite some limitations, such as potential biases and challenges with accuracy in the long-time evolution, otVMC offers a robust tool for studying the dynamics of large, strongly interacting systems and holds promise for future extensions to continuous and higher-dimensional systems.","abstract_has_math":false,"creators":["D'ALBERTO, JACOPO"],"institution":"Università degli Studi di Milano","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["supervisore: D. E. Galli ; co-supervisore: G. Bertaina ; director of the school: A. Mennella","J. 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Indeed, tra- ditional computational methods struggle with the exponential growth of Hilbert space in these systems. This thesis introduces the Open-Time Variational Monte Carlo (otVMC) method, which combines the quantum trajectory formalism with Monte Carlo tech- niques to enable real-time simulations of open quantum systems. By exploiting stochas- tic Schrödinger equations and a variational approach, otVMC significantly reduces com- putational complexity. Applied to a dissipative many-body spin system with long-range interactions, this method successfully simulates up to 180 spins and provides insights into time evolution of the spin-squeezing parameter. 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