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1. PathSum : A C++ and Fortran suite of fully quantum mechanical real-time path integral methods for (multi-)system + bath dynamics

   https://doi.org/10.1063/5.0151748  

   Kundu, Sohang; Makri, Nancy (June 2023, The Journal of Chemical Physics)

   This paper reports the release of PathSum, a new software suite of state-of-the-art path integral methods for studying the dynamics of single or extended systems coupled to harmonic environments. The package includes two modules, suitable for system–bath problems and extended systems comprising many coupled system–bath units, and is offered in C++ and Fortran implementations. The system–bath module offers the recently developed small matrix path integral (SMatPI) and the well-established iterative quasi-adiabatic propagator path integral (i-QuAPI) method for iteration of the reduced density matrix of the system. In the SMatPI module, the dynamics within the entanglement interval can be computed using QuAPI, the blip sum, time evolving matrix product operators, or the quantum–classical path integral method. These methods have distinct convergence characteristics and their combination allows a user to access a variety of regimes. The extended system module provides the user with two algorithms of the modular path integral method, applicable to quantum spin chains or excitonic molecular aggregates. An overview of the methods and code structure is provided, along with guidance on method selection and representative examples. 

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2. Path Integral over Equivalence Classes for Quantum Dynamics with Static Disorder

   https://doi.org/10.1021/acs.jpclett.3c03555  

   Makri, Nancy (February 2024, The Journal of Physical Chemistry Letters)

   An efficient, fully quantum mechanical real-time path integral method for including the effects of static disorder in the dynamics of systems coupled to common or local harmonic baths is presented. Rather than performing a large number of demanding calculations for different realizations of the system Hamiltonian, the influence of the bath is captured through a single evaluation of the path sum by grouping the system paths into equivalence classes of fixed system amplitudes. The method is illustrated with several analytical and numerical examples that show a variety of nontrivial effects arising from the interplay among coherence, dissipation, thermal fluctuations and geometric phases. 

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3. On the lapse contour in the gravitational path integral

   https://doi.org/10.1103/PhysRevD.111.066014  

   Banihashemi, Batoul; Jacobson, Ted (March 2025, Physical Review D)

   The gravitational path integral is usually implemented with a covariant action by analogy with other gauge field theories, but the gravitational case is different in important ways. A key difference is that the integrand has an essential singularity, which occurs at zero lapse where the spacetime metric degenerates. The lapse integration contour required to impose the local time reparametrization constraints must run from $-\infty$to $+\infty$, yet must not pass through zero. This raises the question: for an application—such as a partition function—where the constraints should be imposed, what is the correct integration contour, and why? We study that question by starting with the reduced phase space path integral, which involves no essential singularity. We observe that if the momenta are to be integrated before the lapse, to obtain a configuration space path integral, the lapse contour should pass below the origin in the complex lapse plane. This contour is also consistent with the requirement that quantum field fluctuation amplitudes have the usual short distance vacuum form, and with obtaining the Bekenstein-Hawking horizon entropy from a Lorentzian path integral. Published by the American Physical Society2025 

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4. Renormalization and running in the 2D CP (1) model

   https://doi.org/10.1007/JHEP02(2025)146  

   Buccio, Diego; Donoghue, John F; Menezes, Gabriel; Percacci, Roberto (February 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We calculate the scattering amplitude in the two dimensionalCP(1) model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. The results can be extended to theO(N) model, for allN. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories. 

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5. Eshelby’s inclusion and inhomogeneity problems under harmonic heat transfer

   https://doi.org/10.1098/rspa.2024.0824  

   Wu, Chunlin; Wang, Tengxiang; Yin, Huiming (July 2025, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Eshelby’s equivalent inclusion method (EIM) has been formulated to solve harmonic heat transfer problems of an infinite or semi-infinite domain containing an inclusion or inhomogeneity. For the inclusion problem, the heat equation is reduced to a modified Helmholtz’s equation in the frequency domain through the Fourier transform, and the harmonic Eshelby’s tensor is derived from the domain integrals of the corresponding Green’s function in the form of Helmholtz’s potential. Using the convolution property of the Fourier space, Helmholtz’s potential with polynomial-form source densities is integrated over an ellipsoidal inclusion, which is reduced to a one-dimensional integral for spheroids and an explicit, exact expression for spheres. The material mismatch in the inhomogeneity problem is simulated by continuously distributed eigen-fields, namely, the eigen-temperature-gradient (ETG) and eigen-heat-source (EHS) for thermal conductivity and specific heat, respectively. The proposed EIM formulation is verified by the conventional boundary integral method with the harmonic Green’s function and multi-domain interfacial continuity, and the accuracy and efficacy of the solution are discussed under different material and load settings. 

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