Quantum shape effects and novel thermodynamic behaviors at nanoscale

Thermodynamic properties of confined systems depend on sizes of the confinement domain due to quantum nature of particles. Here we show that shape also enters as a control parameter on thermodynamic state functions. By considering specially designed confinement domains, we separate the influences of quantum size and shape effects from each other and demonstrate how shape effects alone modify Helmholtz free energy, entropy and internal energy of a confined system. We propose an overlapped quantum boundary layer method to analytically predict quantum shape effects without even solving Schr\"odinger equation or invoking any other mathematical tools. Thereby we reduce a thermodynamic problem into a simple geometric one and reveal the profound link between geometry and thermodynamics. We report also a torque due to quantum shape effects. Furthermore, we introduce isoformal, shape preserving, process which opens the possibility of a new generation of thermodynamic cycles operating at nanoscale with unique features.

[1]  E. Roduner.  Nanoscopic Materials: Size-Dependent Phenomena , 2006 .

[2]  Wang Yao,et al.  Quantum size effects on the work function of metallic thin film nanostructures , 2010, Proceedings of the National Academy of Sciences.

[3]  C. Stamm,et al.  Quantum oscillations in a confined electron gas , 1997, Nature.

[5]  F. Peeters,et al.  Dependence of superconducting properties on the size and shape of a nanoscale superconductor: from nanowire to film , 2007 .

[6]  Quantum force induced on a partition wall in a harmonic potential , 2009, 0906.2626.

[7]  Han Xiao,et al.  The effect of the size and shape on the bond number of quantum dots and its relationship with thermodynamic properties. , 2015, Physical chemistry chemical physics : PCCP.

[8]  A. M. Fennimore,et al.  Rotational actuators based on carbon nanotubes , 2003, Nature.

[9]  Ronnie Kosloff,et al.  The Quantum Harmonic Otto Cycle , 2016, Entropy.

[10]  Ingo Müller,et al.  The Casimir-like size effects in ideal gases , 2004 .

[11]  Yang Guo,et al.  Superconductivity Modulated by Quantum Size Effects , 2004, Science.

[12]  Peter M. Hoffmann,et al.  Life's Ratchet: How Molecular Machines Extract Order from Chaos , 2012 .

[13]  P. Frigeri,et al.  Quantum size and shape effects on the excited states of In x Ga 1 − x As quantum dots , 2001 .

[14]  D. Nikonov,et al.  Quantum particle in a box with moving walls , 1993 .

[15]  Eberhard R. Hilf,et al.  Spectra of Finite Systems , 1980 .

[16]  V. Colvin,et al.  Shape matters , 2003, Nature materials.

[17]  Niklas Peinecke,et al.  Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids , 2006, Comput. Aided Des..

[18]  Gabriel Zeltzer,et al.  Quantum Phase Extraction in Isospectral Electronic Nanostructures , 2008, Science.

[19]  David L. Webb,et al.  One cannot hear the shape of a drum , 1992, math/9207215.

[20]  Quantum shape effects on Zeeman splittings in semiconductor nanostructures , 2005, cond-mat/0503042.

[21]  Universality of the quantum boundary layer for a Maxwellian gas , 2009 .

[22]  Berry,et al.  Influence of shape on electron transport in ballistic quantum dots. , 1994, Physical review. B, Condensed matter.

[23]  David Gelbwaser-Klimovsky,et al.  Non-equilibrium quantum heat machines , 2015, 1507.01660.

[24]  M. Kardar,et al.  Probing the strong boundary shape dependence of the Casimir force. , 2001, Physical review letters.

[25]  M. Kac.  Can One Hear the Shape of a Drum , 1966 .

[26]  Geometry effects in confined space. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Antti-Pekka Jauho,et al.  Quantum Corrections in Nanoplasmonics: Shape, Scale, and Material. , 2016, Physical review letters.

[28]  A. Sisman,et al.  Discrete nature of thermodynamics in confined ideal Fermi gases , 2014, 1408.1086.

[29]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .

[30]  Jingbo Li,et al.  Shape Effects on Electronic States of Nanocrystals. , 2003, Nano letters.

[31]  L. Buchaillot,et al.  Size and shape effects on creep and diffusion at the nanoscale , 2008, Nanotechnology.

[32]  W. Halperin,et al.  Quantum size effects in metal particles , 1986 .

[33]  Ronnie Kosloff,et al.  Quantum heat engines and refrigerators: continuous devices. , 2013, Annual review of physical chemistry.

[34]  A. Sisman,et al.  Discrete density of states , 2016, Physics Letters A.

[35]  G. Schmid,et al.  Quantum-size effects in the thermodynamic properties of metallic nanoparticles , 1996, Nature.

[36]  G. Kurizki,et al.  Quantum technologies with hybrid systems , 2015, Proceedings of the National Academy of Sciences.

[37]  Kwanoh Kim,et al.  Ultrahigh-speed rotating nanoelectromechanical system devices assembled from nanoscale building blocks. , 2014, Nature communications.

[38]  A. Croy,et al.  Dynamics of a nanoscale rotor driven by single-electron tunneling , 2012, 1204.5918.

[39]  Altug Sisman,et al.  Quantum forces of a gas confined in nano structures , 2013 .

[40]  R. Arita,et al.  Emergent quantum confinement at topological insulator surfaces , 2012, Nature Communications.

[41]  Ronnie Kosloff,et al.  Quantum Flywheel , 2016, 1602.04322.

[42]  T. Harayama,et al.  ‘Can one hear the shape of a drum?’: revisited , 2005 .

[43]  V. Vedral,et al.  Classification of macroscopic quantum effects , 2014, 1406.0659.

[44]  G. Refael,et al.  Adiabatic quantum motors. , 2013, Physical review letters.

[45]  J. Rossnagel,et al.  A single-atom heat engine , 2015, Science.

[46]  Nathalie Katsonis,et al.  Molecular machines: Nanomotor rotates microscale objects , 2006, Nature.

[47]  Wu-Sheng Dai,et al.  The pressure exerted by a confined ideal gas , 2011 .

[48]  K. Nakamura,et al.  Ideal quantum gas in an expanding cavity: nature of nonadiabatic force. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  K. Thas,et al.  Hearing shapes of drums — mathematical and physical aspects of isospectrality , 2010, 1101.1239.

[50]  Altug Sisman,et al.  Quantum boundary layer: a non-uniform density distribution of an ideal gas in thermodynamic equilibrium , 2007 .

[51]  Jianzhong Wu,et al.  Shape effect on nanoparticle solvation: a comparison of morphometric thermodynamics and microscopic theories. , 2012, Langmuir : the ACS journal of surfaces and colloids.

[52]  D. Kendall.  The diffusion of shape , 1977, Advances in Applied Probability.

[53]  F. Peeters,et al.  Atypical BCS-BEC crossover induced by quantum-size effects , 2012, 1203.3325.

[54]  G. Milburn,et al.  Macroscopic Quantum Resonators (MAQRO): 2015 update , 2015, 1503.02640.

[55]  A. Sisman,et al.  Thermosize potentials in semiconductors , 2017, 1705.05695.

[56]  P. Reimann,et al.  Brownian gyrator: a minimal heat engine on the nanoscale. , 2007, Physical review letters.

[57]  W. Wurth,et al.  Quantum size effects of small, size-selected and deposited CoRh clusters on Ni , 2016 .

[58]  X. Yi,et al.  Dynamics of quantum-classical hybrid systems: Effect of matter-wave pressure , 2009, 0910.4061.