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oai:figshare.com:article/33902713 2026-09-17T17:05:59Z category_1 category_915 category_13 category_21 category_873 category_734 category_811 category_64 category_128 portal_63 item_type_3 month_year_09_2026

The Potential Energy Landscape Formalism for Quantum Liquids in the Continuous Ring-Polymer Limit Yang Zhou (65942) Gustavo E. Lopez (14408055) Nicolas Giovambattista (1745482) Biophysics Physical Sciences not elsewhere classified Genetics Biotechnology Chemical Sciences not elsewhere classified Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Cancer Hematology normal mode frequencies corresponding frequencies given >, commonly used >< sub >< potential energy landscape ></ sub >. ></ sub >, ></ sub >); helmholtz free energy → ∞ provides main pel properties statistical mechanics ). classical liquid counterpart pel formalism reduces harmonic approximation </ ></ sub free energy → ∞ statistical mechanics harmonic approximation converge ). harmonic pel thermodynamic behavior theoretical framework quantum liquids quantum liquid previous version previous studies new version mapped onto formalism (< expressed analytically e ., developed assuming computer simulations The potential energy landscape (PEL) formalism is a powerful tool within statistical mechanics to study the thermodynamic behavior of classical and quantum liquids as well as non-annealing glasses. In the quantum case, this theoretical framework is based on the path-integral formulation of statistical mechanics where the liquid/non-annealing glass is mapped onto a classical system of ring-polymers. In previous studies, and motivated by path-integral (PI) computer simulations, the PEL formalism was developed assuming that the ring-polymers were discrete, i.e., each ring-polymer was composed of a finite number of beads, <i>n</i>_<i>b</i>. In this work, we revisit the PEL formalism for the case where the ring-polymers of the system are continuous, i.e., <i>n</i>_<i>b</i> → ∞ (as required in the PI formulation of statistical mechanics). We find that in this limit, the PEL of the quantum liquid is unique and well-defined. The main PEL properties of the system, including the average inherent structure energy <i>E</i>_<i>IS</i>, configurational entropy <i>S</i>_<i>IS</i>, and vibrational Helmholtz free energy <i>F</i>_<i>vib</i>, are also well-defined (i.e., they converge). Notably, in the harmonic approximation of the PEL, <i>F</i>_<i>vib</i> can be expressed analytically; it is identical to the free energy of a multidimensional quantum harmonic oscillator with the corresponding frequencies given by the normal mode frequencies of the classical liquid counterpart (accessible from classical computer simulations). When applied to non-annealing glasses and crystals, this new version of the PEL formalism reduces to the so-called <i>quasi-harmonic approximation</i>, commonly used in the study of solids. Overall, the PEL formalism for <i>n</i>_<i>b</i> → ∞ provides an alternative approach to its previous version (finite <i>n</i>_<i>b</i>); it is also more elegant and intuitive, and simpler to apply. For a Gaussian and harmonic PEL, this formalism (<i>n</i>_<i>b</i> → ∞) allows one to obtain the Helmholtz free energy of the quantum liquid using classical computer simulations, avoiding the more expensive PI computer simulations. 2026-09-17T00:00:00Z Dataset Dataset 10.1021/acs.jctc.6c01077.s001 https://figshare.com/articles/dataset/The_Potential_Energy_Landscape_Formalism_for_Quantum_Liquids_in_the_Continuous_Ring-Polymer_Limit/33902713 CC BY-NC 4.0