Gas-induced friction and diffusion of rigid rotors.

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

[1]  J. Ignacio Cirac,et al.  Optically Levitating Dielectrics in the Quantum Regime: Theory and Protocols , 2010, 1010.3109.

[2]  G. Mulholland,et al.  Rotational Diffusion Coefficient (or Rotational Mobility) of a Nanorod in the Free-Molecular Regime , 2014 .

[3]  Fred L. Whipple,et al.  A comet model. I. The acceleration of Comet Encke , 1950 .

[4]  内山 健太郎,et al.  26 , 2015, Magical Realism for Non-Believers.

[5]  C. Cercignani.  The Boltzmann equation and its applications , 1988 .

[6]  B. Dahneke.  Slip correction factors for nonspherical bodies—II free molecule flow , 1973 .

[7]  G. Ciani,et al.  Gas damping force noise on a macroscopic test body in an infinite gas reservoir , 2009, 0907.5375.

[8]  Stefan Kuhn,et al.  Optically driven ultra-stable nanomechanical rotor , 2017, Nature Communications.

[9]  D. McClelland,et al.  LISA pathfinder appreciably constrains collapse models , 2016, 1606.03637.

[10]  Jonghoon Ahn,et al.  Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States. , 2017, Physical review letters.

[11]  Jonghoon Ahn,et al.  Torsional Optomechanics of a Levitated Nonspherical Nanoparticle. , 2016, Physical review letters.

[12]  M. Paternostro,et al.  Proposal for a noninterferometric test of collapse models in optomechanical systems , 2014, 1402.5421.

[13]  W. Dimpfl,et al.  Large angle inelastic scattering of Na+ by D2 , 1974 .

[14]  Y. Alibert,et al.  The photophoretic sweeping of dust in transient protoplanetary disks , 2012 .

[15]  K. Hammerer,et al.  Optomechanical sensing of spontaneous wave-function collapse. , 2014, Physical review letters.

[16]  Strong coupling between a single nitrogen-vacancy spin and the rotational mode of diamonds levitating in an ion trap , 2017, 1702.00774.

[17]  Henrik Stapelfeldt,et al.  Colloquium: Aligning molecules with strong laser pulses , 2003 .

[18]  Angelo Bassi,et al.  Models of Wave-function Collapse, Underlying Theories, and Experimental Tests , 2012, 1204.4325.

[19]  A. Bassi,et al.  Experimental bounds on collapse models from gravitational wave detectors , 2016, 1606.04581.

[20]  B. Stickler,et al.  Quantum angular momentum diffusion of rigid bodies , 2017, 1712.05596.

[21]  Stefan Kuhn,et al.  Cavity cooling of free silicon nanoparticles in high vacuum , 2013, Nature Communications.

[22]  Mauro Paternostro,et al.  Parametric feedback cooling of levitated optomechanics in a parabolic mirror trap , 2016, 1603.02917.

[23]  W. Schepper,et al.  Rotationally inelastic, classical scattering from an anisotropic rigid shell potential of rotation symmetry , 1979 .

[24]  G. E. Cook.  The effect of aerodynamic lift on satellite orbits , 1964 .

[25]  M. Raizen,et al.  Measurement of the Instantaneous Velocity of a Brownian Particle , 2010, Science.

[26]  Peter Roberts,et al.  Spacecraft drag modelling , 2014 .

[27]  Abdullah Al Mamun,et al.  Introduction to Dusty Plasma Physics , 2001 .

[28]  R Kaltenbaek,et al.  Large quantum superpositions and interference of massive nanometer-sized objects. , 2011, Physical review letters.

[29]  G. Wurm,et al.  SELF-SUSTAINED RECYCLING IN THE INNER DUST RING OF PRE-TRANSITIONAL DISKS , 2016, 1609.03475.

[30]  T. S. Monteiro,et al.  Cavity cooling a single charged levitated nanosphere. , 2015, Physical review letters.

[31]  A. Geraci,et al.  Zeptonewton force sensing with nanospheres in an optical lattice , 2016, 1603.02122.

[32]  M. Paternostro,et al.  Testing Wavefunction Collapse Models using Parametric Heating of a Trapped Nanosphere , 2015, 1506.08782.

[33]  D. Bodewits,et al.  A rapid decrease in the rotation rate of comet 41P/Tuttle–Giacobini–Kresák , 2018, Nature.

[34]  T. S. Monteiro,et al.  Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles. , 2015, Physical review letters.

[35]  D. E. Chang,et al.  Cavity opto-mechanics using an optically levitated nanosphere , 2009, Proceedings of the National Academy of Sciences.

[36]  Petr Pravec,et al.  The tumbling rotational state of 1I/‘Oumuamua , 2017, Nature Astronomy.

[37]  H. Risken.  Fokker-Planck Equation , 1996 .

[38]  Franck Laloe,et al.  Heating of trapped ultracold atoms by collapse dynamics , 2014, 1409.5388.

[39]  J. Anders,et al.  Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere. , 2013, Nature nanotechnology.

[40]  Stefan Kuhn,et al.  Cavity-Assisted Manipulation of Freely Rotating Silicon Nanorods in High Vacuum , 2015, Nano letters.

[41]  Colin Tudge,et al.  Planet , 1999 .

[42]  J. Ignacio Cirac,et al.  Toward quantum superposition of living organisms , 2009, 0909.1469.

[43]  H. Essén,et al.  Force on a spinning sphere moving in a rarefied gas , 2003 .

[44]  Mark G. Raizen,et al.  Millikelvin cooling of an optically trapped microsphere in vacuum , 2011, 1101.1283.

[45]  W. Schepper,et al.  Rotationally inelastic, classical rigid shell scattering , 1981 .

[46]  D. Vitali,et al.  Discriminating the effects of collapse models from environmental diffusion with levitated nanospheres , 2015, 1508.00466.

[47]  J. Ortiz,et al.  Long-term simulations of the rotational state of small irregular cometary nuclei , 2003 .

[48]  A. Heptonstall,et al.  Increased Brownian force noise from molecular impacts in a constrained volume. , 2009, Physical review letters.

[49]  R. Bernstein,et al.  Classical Study of Rotational Excitation of a Rigid Rotor: Li+ + H2 , 1971 .

[50]  Stefan Kuhn,et al.  Full Rotational Control of Levitated Silicon Nanorods , 2016, 1608.07315.

[51]  Florian Blaser,et al.  Cavity cooling of an optically levitated submicron particle , 2013, Proceedings of the National Academy of Sciences.

[52]  L. Diósi.  Testing spontaneous wave-function collapse models on classical mechanical oscillators. , 2014, Physical review letters.

[53]  B. E. Kane.  Levitated spinning graphene flakes in an electric quadrupole ion trap , 2010, 1006.3774.

[54]  Christoph Dellago,et al.  Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state. , 2014, Nature nanotechnology.

[55]  Representation and calculation of photophoretic forces and torques , 1995 .

[56]  P. S. Epstein,et al.  On the Resistance Experienced by Spheres in their Motion through Gases , 1924 .

[57]  James Bateman,et al.  Near-field interferometry of a free-falling nanoparticle from a point-like source , 2013, Nature Communications.

[58]  B. Stickler,et al.  Collapse-induced orientational localization of rigid rotors [Invited] , 2017, 1702.00181.

[59]  P. Kam,et al.  : 4 , 1898, You Can Cross the Massacre on Foot.

[60]  Fokker-Planck operator for free-molecular, nonspherical, thermally nonequilibrium Brownian particles , 2008 .

[61]  H. Rohatschek,et al.  Semi-empirical model of photophoretic forces for the entire range of pressures , 1995 .

[62]  G. Morfill,et al.  Complex plasmas: An interdisciplinary research field , 2009 .

[63]  Larry Denneau,et al.  A brief visit from a red and extremely elongated interstellar asteroid , 2017, Nature.

[64]  Lukas Novotny,et al.  Subkelvin parametric feedback cooling of a laser-trapped nanoparticle. , 2012, Physical review letters.