We propose a reinterpretation and reformulation of the single-particle Green's function in nonrelativistic quantum many-body theory with an emphasis on normalization. By downfolding a correlation function covering all of Fock space into the observable portion, we derive a nonlocal Dyson equation which depends on an unknown downfolding frequency. The downfolding frequency is determined by solving the inverse problem so that the spectral function of the single-particle propagator is a Dirac-$δ$ function. Upon measurement, the system collapses stochastically onto one of these normalized solutions. This collapse has a nonlocal effect on the path the particle takes, in agreement with quantum entanglement. We postulate that the multiplicity of each quantized solution is directly related to the ensemble averaged spectrum and the entropy created by measurement of the particle. In the final part, we outline a new picture of dynamics in quantum many-body systems. As a function of the coupling strength, the multiplicity for collapse has a complicated form due to the shape of the quantization condition. This structure creates an entropic force from counting quantized solutions which is predominantly attractive but likely also has a narrow repulsive regime at weak coupling. Upon collapse, an internal spacetime forms between the two points in order to carry the information gained from the reduction of the probabilistic many-body state. The repeated creation of these spacetime bridges defines an internal spacetime with a complicated shape and history. We treat the quantum system as a finite informational resource that holds information about possible normalized outcomes, collapses the wave function to reset after encountering a conflict, and creates an internal spacetime to carry the information gained with every collapse.
We propose a reinterpretation and reformulation of the single-particle Green's function in nonrelativistic quantum many-body theory with an emphasis on normalization. By downfolding a correlation function covering all of Fock space into the observable portion, we derive a nonlocal Dyson equation which depends on an unknown downfolding frequency. The downfolding frequency is determined by solving the inverse problem so that the spectral function of the single-particle propagator is a Dirac-δ function. Upon measurement, the system collapses stochastically onto one of these normalized solutions. This collapse has a nonlocal effect on the path the particle takes, in agreement with quantum entanglement. We postulate that the multiplicity of each quantized solution is directly related to the ensemble averaged spectrum and the entropy created by measurement of the particle. In the final part, we outline a new picture of dynamics in quantum many-body systems. As a function of the coupling strength, the multiplicity for collapse has a complicated form due to the shape of the quantization condition. This structure creates an entropic force from counting quantized solutions which is predominantly attractive but likely also has a narrow repulsive regime at weak coupling. Upon collapse, an internal spacetime forms between the two points in order to carry the information gained from the reduction of the probabilistic many-body state. The repeated creation of these spacetime bridges defines an internal spacetime with a complicated shape and history. We treat the quantum system as a finite informational resource that holds information about possible normalized outcomes, collapses the wave function to reset after encountering a conflict, and creates an internal spacetime to carry the information gained with every collapse.
Abstract We show that there is a hidden freedom in quantum many-body theory associated with overcompleteness of the time evolution through the single-particle subspace of a many-body system. To fix the freedom, an additional constraint is necessary. We argue that the appropriate constraint on the time evolution through the subspace is to quantize the propagation of entangled pairs of particles, represented by the single-particle spectral function, instead of individual particles. This solution method creates a surface that indicates the multiplicity of every solution to the inverse problem defined by matching the freedom to the constraint. Upon measurement, the system collapses nonlocally onto a single quantized solution. In addition to a combinatoric multiplicity, each solution acquires a multiplicity due to its stability when subject to a small variation in the microscopic degrees of freedom. Numerical calculations for a two-level system show that our theory improves upon standard theory in the description of non-quasiparticle spectral features. Our reinterpretation of quantum many-body theory is not based on the Born rule and offers a more faithful representation of experiments than current theory by modeling individual, quantized events with an explicit collapse model.
The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic nature of nonlocal effects prevents the superluminal transmission of information, while nonlocal entanglement relations provide a means to enforce conservation laws in a probabilistic theory. In order to explain measurement-induced changes in terms of fundamental physical processes it is important to take these two key characteristics into account. One way to do this is to modify the Schroedinger equation by adding stochastic, nonlinear terms. A number of such proposals have been made over the past few decades. A recently proposed equation based on the assumption that wave function collapse is induced by a sequence of correlating interactions of the kind that constitute measurements has been shown to maintain strict adherence to conservation laws in individual instances, and has also eliminated the need to introduce any new, ad hoc physical constants. In this work it is shone that the proposed stochastic modification to the Schroedinger equation is also Lorentz invariant, even though it is formulated in a preferred reference frame. It is further argued that the additional spacetime structure that the proposed modification requires provides a way to implement the assumption that spacelike-separated operators (and measurements) commute, and that this assumption of local commutativity should be regarded as a third postulate of relativity.
Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) G W approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime.
The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way. Among the most striking features of the entanglement entropy are its unbounded linear growth in the thermodynamic limit, its asymptotic extensivity in finite-size systems, and the possibility of measurement-induced phase transitions, all of which have no obvious classical counterpart. Here, we show how these key qualitative features emerge naturally also in classical information spreading, as long as one treats the classical many-body problem on par with the quantum one, that is, by explicitly accounting for the exponentially large classical probability distribution. Our analysis is supported by extensive numerics on prototypical cellular automata and Hamiltonian systems, for which we focus on the classical mutual information and also introduce a ``classical entanglement entropy.'' Our study sheds light on the nature of information spreading in classical and quantum systems, and opens avenues for quantum-inspired classical approaches across physics, information theory, and statistics.
Classical statistical mechanics relies on the ergodic hypothesis, which states that a system explores the entire allowed phase space during its time evolution. Pure quantum states are at odds with this concept as they remain in a single quantum state even if the system's parameters are suddenly altered. However, in a generic many-body system, coherent dynamics drive local thermalization of its subsystems. In this case, any local observable appears thermal and can be described by a statistical ensemble even though the full state remains pure. The key to understanding the phenomenon of quantum thermalization lies in the entanglement properties of the system: The presence of entanglement creates local entropy that validates the use of statistical physics.\nIn this thesis, we experimentally study the emergence of statistical mechanics in a quantum state and observe the fundamental role of quantum entanglement in facilitating this emergence. We perform microscopy on an evolving quantum system, and we see thermalization occur on a local scale while we measure that the full quantum state remains pure.\nThe only known robust exception from the paradigm of quantum thermalization is provided by disordered systems. In this case, the particle transport ceases through the system, preventing the formation of a sufficient amount of entanglement required for thermalization. However, if the many-body system is interacting, the state develops non-local quantum correlations that are inaccessible to any local observable. These correlations spread exponentially slowly in time throughout the entire system and are considered a hallmark feature of many-body-localized states.\nIn order to study the interplay between thermalization and localization in our system, we develop novel methods for high fidelity state preparation and readout. We achieved an exquisite isolation of our system from the environment, which allows us to monitor coherent many-body dynamics over multiple decades of time evolution.\nWe experimentally realize such a many-body localized system and observe the formation of non-local quantum correlations, while the particle transport is frozen in the system. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in non-interacting, disordered systems.
This is Paper 143 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops the mechanics of entanglement in pq-spacetime from the finite closure structure established in Paper 142. For a bipartite system, the outcome-resolved future histories form a joint amplitude ledger whose normalized Gram spectrum defines the cross-boundary closure spectrum. This spectrum provides a basis-independent foundation for Schmidt rank, entanglement entropy, purity, and the effective number of participating closure sectors. Entanglement entropy is therefore not a raw count of microscopic histories or boundary crossings. The histories must first interfere through their Z4 phases, after which the surviving orthogonal closure sectors determine the observable entropy. The singlet boundary consequently carries two equal closure weights and entropy ln 2. The paper also derives a finite boundary-capacity bound, distinguishes decoherence from disentanglement, and explains long-distance persistence as invariance under local norm-preserving evolution rather than as a force acting across space. Decoherence occurs when environmental boundary enlargement creates distinguishable records and suppresses accessible phase relations. Finally, geometry and entanglement are identified as distinct invariants of the same finite β-boundary structure: geometry is read from transfer-kernel moments, while entanglement is read from the closure spectrum. No adjustable collapse rate, distance-decay law, area coefficient, or finite correction to standard quantum correlations is introduced.