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I investigate the tunneling decay rate of a polaritonic system formed by a strong coupling between a vacuum cavity mode and $N$ metastable systems. Using a simple model potential, I find the instanton solutions controlling the low-temperature tunneling rate. The resulting rate modification due to the cavity is proportional to the mean of the second power of the light-matter coupling. No collective effect that would enhance the rates by a factor of $\sqrt{N}$ is present, which is in line with the results in the thermal activation regime., Minor text changes compared to previous version

Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum condensates, the nature of the transition between the quasiclassical dynamics at large scales and the corresponding dynamics at small scales, where the quantization of vorticity is essential, remains an outstanding unresolved question. Here we expand the paradigm of wave-driven turbulence to rotating quantum fluids where the spectrum of waves extends to microscopic scales as Kelvin waves on quantized vortices. We excite inertial waves at the largest scale by periodic modulation of the angular velocity and observe dissipation-independent transfer of energy to smaller scales and the eventual onset of the elusive Kelvin-wave cascade at the lowest temperatures. We further find that energy is pumped to the system through a boundary layer distinct from the classical Ekman layer and support our observations with numerical simulations. Our experiments demonstrate a new regime of turbulent motion in quantum fluids where the role of vortex reconnections can be neglected, thus stripping the transition between the classical and the quantum regimes of turbulence down to its bare bones., Comment: 21 pages, 11 figures

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg–Kohn theorem is found void, in general, while many insights into the topological structure of the density-potential mapping can be won. We give precise conditions for a ground state to be uniquely v-representable and are able to prove that this property holds for almost all densities. A set of examples illustrates the theory and demonstrates the non-convexity of the pure-state constrained-search functional. peerReviewed

The diamagnetic susceptibility is an essential magnetic property, as it describes magnetization response of material to an external magnetic field. However, accurate computational data is not available for systems at finite temperatures, because nuclear motion and finite temperature are not well-supported by common ab initio simulation methods. We utilize path integral Monte Carlo method (PIMC), which combines non-relativistic quantum mechanics with statistical mechanics at finite temperatures. PIMC takes exact many-body effects into account, which brings precise simulation of electronic correlation and non-adiabatic nuclei. The accuracy of results is limited by statistical error, which can be controlled with the extent of computation. In this work, we formulate path integrals and derive an estimator for diamagnetic susceptibility in the limit of zero magnetic field. The estimator is applied in PIMC simulations, and the diamagnetic susceptibility is calculated for He, H, H2, H2+, D2, HD, Ps and Ps2, where D is a deuterium and Ps is a positronium. The systems are simulated both with nonadiabatic nuclei and with fixed Born--Oppenheimer nuclei. Temperature is varied on range from 300 K to 3000 K. The hydrogen atom and the hydrogen molecule express significant nonadiabatic effects in diamagnetic susceptibility, but the helium atom does not. The susceptibility of monatomic systems do not correlate with the temperature, which is expected. The susceptibility of diatomic molecules increases at higher temperatures, which can be explained by a nuclear separation caused by centrifugal forces. The susceptibility of positronium decreases at higher temperatures, which is unexpected. Obtained PIMC results are compared to 0 K reference values, because there are nearly no published calculations available at finite temperatures. If the PIMC results are extrapolated at 0 K, they are fairly well in line with the reference values. Overall, PIMC appears to be a good method for calculating exact diamagnetic properties of small molecules.

We propose here a fully backaction-evading scheme for the measurement of the entanglement between two nanomechanical resonators. The system, which consists of two mechanical oscillators, coupled to a single mode of an electromagnetic resonant cavity through a radiation-pressure interaction term, is driven by two pump tones and four detection tones. As previously discussed in the literature, the former induce entanglement between the two mechanical oscillators, while we show here that a specific choice of phase and amplitude of the detection tones allows for direct pairwise reconstruction of the collective quadrature fluctuations of the mechanical oscillators belonging to quantum-mechanics-free subspaces, thereby providing direct evidence of the entanglement properties of the two mechanical resonators., 8 pages, 4 figures, accepted for publication in Physical review A

Kvanttimekaniikka edustaa tämänhetkistä parasta tietoa siitä, kuinka luonto toimii. Se on erityisen tärkeää elektronirakennelaskennassa, jossa klassinen mekaniikka ei enää toimi. Vaikka teoria on hyvin tunnettu, ainoastaan pieni joukko ongelmia voidaan ratkaista eksaktisti, minkä vuoksi joudutaan turvautumaan approksimaatioihin ja numeerisiin menetelmiin. Feymanin polkuintegraalimuotoilu tarjoaa intuitiivisen lähestymistavan epärelativistiseen kvanttimekaniikkaan. Sen pohjana ovat paikka ja aika, ja siihen monen kappaleen kvantti-ilmiöt sisältyvät läpinäkyvästi. Kun kyseessä on formalismi, joka perustuu moniulotteisiin integraaleihin, tehokkaat Monte Carlo tekniikat tarjoavat luonnollisen keinon numeeriseen laskentaan. Tässä väitöskirjassa esitetään uusi menetelmä siihen, kuinka polkuintegraaliformalismia voidaan käyttää kvanttihiukkasten dynamiikan ja tilojen simulointiin, jopa elektroneille. Ensiksi annetaan lyhyt johdanto polkuintegraaleihin ja Monte Carlo -simulointeihin. Suuri osa tästä teoriasta löytyy kvanttimekaniikan oppikirjoista, mutta se on sisällytetty tähän, jotta tämä työ voisi toimia itsenäisenä alustuksena kenelle tahansa, joka on kiinnostunut polkuintegraalisimuloinneista. Seuraavaksi tarkastellaan imaginääriajan menetelmiä, jotka ovat osoittautuneet menestyksellisiksi tehtäessä statis- tisen fysiikan simulaatioita monen kappaleen kvanttisysteemille. Sitten paneudutaan reaaliajan polkuintegraalien haasteisiin ja esitellään uudet menetelmät neljästä alkuperaisestä julkaisusta ja demonstroidaan niiden käyttöä. Seuraavaksi tarkastellaan reaaliajan polkuintegraalimenetelmiin liittyviä ongelmia ja esitetään joitakin keinoja näiden ratkaisemiseksi, sellaisia kuten aaltofunktion oh- jaama otanta ja "levennetty walker" propagaattorin parantamiseksi. "Epäkoherentti propagaatio" esitellään uudenlaisena menetelmänä stationääristen ominaistilojen etsimiseksi. Tämän avulla voidaan etsiä myös viritystiloja, toisin kuin tavanomaisil- la kvantti-Monte Carlo -menetelmillä. Esiteltyjä tekniikoita sovelletaan Hooken atomiin, vahvan korrelaation systeemin, joka on haastava perinteisille lähestymistavoille. Perustilan ja alimpien viritystilojen simuloinnit antavat erinomaiset tulokset tilojen energioille. Myös koherenttia dynamiikkaa simuloidaan ajasta riippuvassa sähkökentässä. Sitten esitellään kuinka perinteinen diffuusio-Monte Carlo -menetelmä ja epäkoherentti propagaatio voidaan yhdistää. Reaaliajan polkuintegraalilaskuja vaivaa positiivisen jakautumafunktion puuttuminen. Tämän ongelman lieventämiseksi esitellään uudenlainen reaaliajan propagaattorin todennäköisyystulkinta ja menetelmä, jota kutsutaan “reaaliajan diffuusio- Monte Carlo -menetelmäksi”. Tätä menetelmää demonstroidaan simuloimalla yksiulotteisen harmonisen oskillaattorin aikaevoluutiolla ja etsitään viritystiloja käyttäen epäkoherenttia propagaatiota. Quantum mechanics represents our current best knowledge of how Nature works. It is especially important for the electronic structure calculations, where classical mechanics breaks down. Even though the theory is well known, only handful of problems can be solved exactly, so approximations and numerical methods are required. Feynman path integral approach offers an intuitively welcome description of nonrelativistic quantum mechanics, rooted in space and time, where quantum manybody effects are included transparently. The formalism based on multidimensional integrals naturally calls for the powerful Monte Carlo techniques to be applied when numerical calculations are performed. In this thesis we present a new approach how real time path integral formalism can be applied to simulate dynamics and states of quantum particles, even electrons. We first give a brief introduction to the theory of path integrals and Monte Carlo simulations. Much of this theory can be found in textbooks of quantum mechanics but it is included here for completeness, so that this work could serve as a selfcontained introduction to anyone interested in path integral simulations. Second, we discuss the imaginary time methods which have proven to be successful in simulations of statistical physics description of the quantum many-particle systems. Finally, we delve into the challenges of the path integrals in real time domain and present the novel methods from the four original papers with demonstrations. The challenges associated with the real time path integral methods are discussed and we present approaches for solving some of these, such as the wave function guided sampling and "widening" of walkers to improve the propagator. We also introduce a novel method for finding stationary eigenstates of quantum systems, called "incoherent propagation". This approach can be used to find the excited states, unlike the conventional Quantum Monte Carlo methods. Presented techniques are then applied to the Hooke’s atom, a system of strong correlation, that is challenging for conventional approaches. Simulations of the ground state and lowest excited states of Hooke’s atom give excellent results for energetics. We also demonstrate simulation of coherent quantum dynamics at the presence of an external transient electric field. We also introduce how conventional diffusion Monte Carlo (DMC) method can be combined with incoherent propagation. Not having a positive sampling distribution is a problem that plagues real time path integral calculations. To alleviate this problem, we introduce a novel probabilistic interpretation of the real time propagator and an approach called "real time diffusion Monte Carlo method". This method is demonstrated in simulation of the time evolution of one dimensional harmonic oscillator and in finding eigenstates of the system using it in conjunction with incoherent propagation.

Under a strong quantum measurement, the motion of an oscillator is disturbed by the measurement back-action, as required by the Heisenberg uncertainty principle. When a mechanical oscillator is continuously monitored via an electromagnetic cavity, as in a cavity optomechanical measurement, the back-action is manifest by the shot noise of incoming photons that becomes imprinted onto the motion of the oscillator. Following the photons leaving the cavity, the correlations appear as squeezing of quantum noise in the emitted field. Here we observe such "ponderomotive" squeezing in the microwave domain using an electromechanical device made out of a superconducting resonator and a drumhead mechanical oscillator. Under a strong measurement, the emitted field develops complex-valued quantum correlations, which in general are not completely accessible by standard homodyne measurements. We recover these hidden correlations, using a phase-sensitive measurement scheme employing two local oscillators. The utilization of hidden correlations presents a step forward in the detection of weak forces, as it allows to fully utilize the quantum noise reduction under the conditions of strong force sensitivity., Comment: 6 pages, 5 figures and supplementary information

We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulative pollution error can be practically eliminated in the case of harmonic wave problems. The restrictions following from the CFL condition can be bypassed with a local time-stepping scheme. The computational savings are at least one order of magnitude.

The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: Has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the Einsten-Podolsky-Rosen-Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of contexts (closed-open arrangements of the slits) upon the marginal distributions of the random variables involved. The analysis presented is entirely within the framework of abstract classical probability theory (with contextually labeled random variables). The only physical constraint used in the analysis is that a particle cannot pass through a closed slit. The noncontextuality of the double-slit system does not generalize to systems describing experiments with more than two slits: in an abstract triple-slit system, almost any set of observable detection probabilities is compatible with both a contextual scenario and a noncontextual scenario of the particle passing though various combinations of open and closed slits (although the issue of physical realizability of these scenarios remains open). peerReviewed

The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the EPR/Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of contexts (closed-open arrangements of the slits) upon the marginal distributions of the random variables involved. The analysis presented is entirely within the framework of abstract classical probability theory (with contextually labeled random variables). The only physical constraint used in the analysis is that a particle cannot pass through a closed slit. The noncontextuality of the double-slit system does not generalize to systems describing experiments with more than two slits: in an abstract triple-slit system, almost any set of observable detection probabilities is compatible with both a contextual scenario and a noncontextual scenario of the particle passing though various combinations of open and closed slits (although the issue of physical realizability of these scenarios remains open)., Comment: Entropy 2018, 20, 278; doi:10.3390/e20040278

Tässä tutkimuksessa perehdytään K-kertaisesti kiellettyjen uniikkien beetasiirtymien faasiavaruusintegraaleihin. K-kertaisesti kielletyt uniikit beetasiirtymät ovat beetahajoamisten alaryhmä, ja faasiavaruusintegraalit kuvaavat hajoamisreaktion jälkeisiä lopputiloja ja antavat muun muassa tärkeää tietoa siirtymän hajoamisvakiosta. Tutkimuksessa laskettiin numeerisesti faasiavaruusintegraalit useille tunnetuille beetasiirtymille, jotka voivat olla kaksi- tai useampikertaisesti kiellettyjä. Saatua laskentadataa analysoitiin eri näkökulmista. Tärkein näkökulma on kielletyn uniikin beetasiirtymän ja samaa beetahajoamista kuvaavan perus- eli sallitun siirtymän välinen suhde, koska tämä näkökulma antaa parhaiten tietoa K:n vaikutuksesta faasiavaruusintegraaliin. Tulokset viittaavat siihen, että siirtymillä, joiden hajoamisenergia on pieni, sallitut ovat dominoivia. Mutta hajoamisenergiaa kasvatettaessa kiellettyjen siirtymien faasiavaruusintegraalit kasvavat suuremmiksi, ja sitä voimakkaammin, mitä suurempi K on. Seuraavaksi tarkasteltiin kielletyn siirtymän faasiavaruusintegraalin suhdetta siirtymän hajoamisenergiaan, mikä antaa tietoa lopputilojen keskimääräisestä lukumäärästä. Nämä tulokset olivat hyvin samankaltaisia kuin edellisessä näkökulmassa. Hajoamisenergian kasvaessa suhdelukukin kasvaa, ja kasvu on sitä nopeampaa, mitä suurempi K on. Kolmas näkökulma oli vertailla beeta+-siirtymien ja elektronisieppausten faasiavaruusintegraalien välisiä suhteita. Koska nämä kaksi beetasiirtymän lajia voivat tapahtua yhtäaikaa, niiden faasiavaruusintegraalit lasketaan aina yhteen. Aikaisemmin on tiedetty, että hajoamisenergia ja atomin järjestysluku vaikuttavat näiden kahden lajin väliseen suhteeseen. Tämän tutkimuksen perusteella kuitenkin myös kiellettyyden asteella näyttäisi olevan vaikutusta. Korkeampi K vaikuttaisi suosivan elektronisieppauksia. Lopuksi vertailtiin faasiavaruusintegraaleja, joissa on otettu huomioon ytimen elektronipilven aiheuttama varjostus niihin faasiavaruusintegraaleihin, joissa sitä ei ole huomioitu. Tulokset eivät eronneet toisistaan merkittävästi, eikä kiellettyyden aste näyttäisi vaikuttavan niihin mitenkään. Phase space integrals of the K:th forbidden unique beta translations. A topic of this thesis was phase space integrals of K:th forbidden unique beta transitions. K:th forbidden unique beta transitions are a subgroup of the beta decays and phase space integrals depict the final states after a decay and for example give important knowledge about a decay constant of a transition. The phase space integrals for many known beta decays having a two or more times forbidden unique transition was calculated numerically in this thesis. The calculation data was then analyzed through various ways. The most important point of view is a ratio of the phase space integrals between a forbidden transition and an allowed transition of the same decay. That ratio gives most information about how the degree of K affects the phase space integral. According to the results in the transitions with small decay energy the allowed ones were dominating. But when the energy grows the phase space integrals of the forbidden transitions become larger and the increase is the faster the bigger the K is. The next point of view is the ratio between the phase space integral of the forbidden beta decay and the decay energy which gives information about the average number of the final states in transition. These results were similar to the previous point of view. When the decay energy increases the ratio increases too and the bigger is K the faster is the increasing. The third point of view was to compare the ratio between the phase space integrals of beta+ decays and electron captures. Because these two types of beta decays can occur simultaneously theirs phase space integrals always sum up. It is already known that decay energy and the atomic number of the nuclear influence the ratio between these two types. According to this thesis, however, also the degree of the forbiddenness seems to have an influence. Higher degree of K seems to prefer electron captures. Finally phase space integrals without taking into account the screening effect of the electron cloud was compared to those with taking into account. The results didn’t have a significant difference nor the degree of K would seem to have any influence to that.

We propose here a scheme, based on the measurement of quadrature phase coherence, aimed at testing the Clauser-Horne-Shimony-Holt Bell inequality in an optomechanical setting. Our setup is constituted by two optical cavities dispersively coupled to a common mechanical resonator. We show that it is possible to generate EPR-like correlations between the quadratures of the output fields of the two cavities, and, depending on the system parameters, to observe the violation of the Clauser-Horne-Shimony-Holt inequality., Comment: 13 pages and 5 figures (typo fixed)

Loppukesästä 1925 julkaistiin fysiikan aikakausilehdessä Zeitschrift für Physik 15-sivuinen tutkimusartikkeli, joka oli otsikoitu harmittoman kuuloisesti: ”Kinemaattisten ja mekaanisten relaatioiden kvanttiteoreettisesta tulkinnasta”. Artikkelin oli kirjoittanut Werner Heisenberg, ja työ oli kaukana harmittomasta. Siinä luotiin perusta kvanttimekaniikan vallankumoukselle, joka avasi atomin salaisuudet muutaman vuoden kuluessa artikkelin julkaisusta. Millaiseen maailmaan kvanttimekaniikka syntyi, mikä vaikutti sen syntyyn ja millainen henkilö oli Werner Heisenberg?

Kun pyritään tutkimaan musiikin ja kokemuksellisuuden suhdetta, on löydettävä epistemologinen jatkuvuus tarkasteltavien ilmiöiden välille. Jos esimerkiksi musiikin kokemuksellisuus luonnollistetaan muutoksiksi organismissa, eli tarkastellaan fysiologisia vasteita suhteessa aistittavaan ilmiöön, ei ole aina johdonmukaista pyrkiä jäsentämään musiikkia perinteisten kulttuurisidonnaisten musiikkianalyyttisten käsitteiden kautta. Data, joka saadaan fysiologisista vasteista on verrattaen välitöntä suhteessa musiikkianalyyttisiin käsitteisiin. Tutkielman tavoitteena on muodostaa käsitys musiikin kokemuksellisuuden tutkimisen epistemologisista haasteista informaation käsitettä hyödyntäen. Aineistona on ollut musiikkifilosofiaa, havaintomekanismeja, systeemiteoriaa ja informaation filosofiaa käsittelevää kirjallisuutta. Metodina on ensisijaisesti filosofinen tarkastelu, jota on täydennetty musiikin kokemuksellisuuden systeemiteoreettisella hahmotelmalla. Informaation käsitteen avulla musiikki voidaan määritellä perustavanlaatuisesti muutokseksi. Informaation käsitteen todetaan myös avaavan tutkimusmahdollisuuksia eri alojen teorioiden yhdistämisen helpottuessa. Kvanttimekaniikan mittausprosseihin ja systeemiteoreettisesti tarkasteltaviin mentaalisiin systeemeihin kytkeytyvän operaatioiden ei-vaihdannaisuuden käsitteen huomattiin tarjovan mahdollisen sillan tutkimusalan suhteen toisistaan etäisten teorioiden välille, joiden teoreettisessa rakenteessa on kuitenkin merkittäviä yhtymäkohtia. Tarkastellaan myös mahdollisia ongelmia käsitteiden liian yleisen määrittelyn aiheuttaman systemaattisen merkityksen hälvenemisessä.

We analyze the statistics of charge and energy currents and spin torque in a metallic nanomagnet coupled to a large magnetic metal via a tunnel contact. We derive a Keldysh action for the tunnel barrier, describing the stochastic currents in the presence of a magnetization precessing with the rate Ω. In contrast to some earlier approaches, our result is valid for an arbitrary ratio of ℏΩ/kBT. We illustrate the use of the action by deriving spintronic fluctuation relations, the quantum limit of pumped current noise, and consider the fluctuations in two specific cases: the situation with a stable precession of magnetization driven by spin transfer torque, and the torque-induced switching between the minima of a magnetic anisotropy. The quantum corrections are relevant when the precession rate exceeds the temperature T, i.e., for ℏΩ≳kBT. peerReviewed

In this thesis, an approximate method introduced to solve time-dependent many-body problems known as time-dependent many-body perturbation theory is studied. Many-body perturbation theory for interacting electrons and phonons is reviewed. In particular, the electron propagator G and an unconventional two-component phonon propagator, which satisfy coupled integral Dyson equations, are introduced. In practice, the associated integral kernels known as the electron Σ and phonon self-energies need to be approximated. The conserving approximations known as the Hartree (-Fock) and the first and second Born approximations, which respect the continuity equation between the electron density and current, are considered in this work. Time-dependent systems of interest are studied in this thesis by using the integro-differential forms of the Dyson equations referred to as the Kadanoff-Baym Equations (KBE). The Kadanoff-Baym equations are introduced for the electron and phonon propagators unconventionally as coupled firstorder integro-differential equations. It is reviewed how these equations are solved numerically by describing an integration rule, a class of practical methods and a parallel implementation of the numerical method. In addition, documentation of how the Kadanoff-Baym equations allow to solve the Bethe-Salpeter Equation (BSE) with the kernel δΣ/δG for the density response function, is provided. In two of the enclosed publications, we benchmarked observables obtained by using the Hartree and partially and fully self-consistent Born approximations against numerically exact results for the two- site, two-electron Holstein model. In this model, the two electrons which are constrained to move between two lattice sites interact indirectly via the electron-phonon coupling. It was observed that only the fully self-consistent Born approximation could cope qualitatively correctly with the competition between the delocalizing and localizing effects of the kinetic and interaction energies. For the other two approximations, spurious bifurcative symmetry breaking with an associated unbounded density response was observed. Nevertheless, also the self-consistent Born approximation was concluded to fail in describing the bipolaronic behavior of the true system. In the third publication, we benchmarked the Hartree-Fock and second Born approximations against an exact method for the few-site Hubbard and Pariser-Parr-Pople models in which the underlying lattice is inert and the electrons interact amongst themselves directly. It was found that the second Born approximation is capable of describing the so-called correlation induced doubly-excited states. This is not possible for time-local approximations such as Hartree-Fock. In addition to the qualitative results, which highlight successes of the applied simple self-energy approximations, the approximate and exact results were also compared on a more quantitative level. It is the quantitative and qualitative results combined which are used in this thesis to assess the quality of the many-body approximations used, with the aim to better understand when these methods are predictive.

Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each other, forming a momentum-space equivalent of the real-space nexus considered before for helium-3. Close to the nexus the Dirac lines exhibit a transition from type I to type II lines. We consider a general model of stacked honeycomb lattices with the symmetry of Bernal (AB) stacked graphite and show that the structural mirror symmetries in such systems protect the presence of the Dirac lines, and also naturally lead to the formation of the nexus. By the bulk-boundary correspondence of topological media, the presence of Dirac lines lead to the formation of drumhead surface states at the side surfaces of the system. We calculate the surface state spectrum, and especially illustrate the effect of the nexus on these states. peerReviewed

Foldameerit ovat oligomeerejä, joilla on stabiili sekundäärirakenne eli niillä on kyky laskostua. Foldameerien syntetisointi ja karakterisointi on usein melko vaikeaa. Tästä syystä niiden rakenteen ja ominaisuuksien tutkimiseksi on kehitelty useita erilaisia laskennallisia malleja. Laskennalliset menetelmät jakautuvat kvanttimekaniikan menetelmiin ja molekyylidynamiikkaan. Molekyylidynamiikka perustuu klassiseen mekaniikkaan. Siinä yksittäisiä atomeja käsitellään palloina, joilla on muuttumaton varaus. Atomien väliset sidokset on yksinkertaistettu jousiksi, joilla on tasapainotila, joka on sama kuin kokeellinen tai laskennallinen sidospituus. Kvanttimekaniikan menetelmillä voidaan tutkia molekyylien konformaatioiden energioita, kun taas molekyylidynamiikalla pystytään mallintamaan molekyylien tai atomien käytöstä liuos- tai kiinteässä tilassa. Tässä työssä pääpaino on erityisesti molekyylidynamiikan menetelmien hyödyntämisessä foldameerien tutkimuksessa.

The problem of quantum dynamics in open systems has gained attention in recent decades and not the least due to the advances made in quantum transport in molecular systems. The main motivation behind quantum transport and molecular electronics is the futuristic goal to be able at some point to replace, or to complement, the silicon-based technology and to make the electronic devices faster. On a fundamental level, one has to deal with time-dependent processes where electron-electron or electron- phonon interactions are of great importance, and they can cause profound quantitative and qualitative changes on the physical and dynamical properties of electronic systems compared to the non-interacting case. Most of the studies of quantum transport have been focused on the steady-state description while neglecting the short-time dynamics. However, the dynamical effects are of great importance since fast- switching processes play a pivotal role in the operation of future devices. We studied the problem of time-dependent electron transport through the Anderson impurity model by using many-body perturbation theory (MBPT) together with Keldysh Green’s functions as well as with time-dependent density functional theory (TDDFT). These methods were compared with numerically exact time-dependent density-matrix renormalization group (tDMRG) method. We found that the many-body perturbation theory results beyond Hartree-Fock approximation were in close agreement with tDMRG results. In addition we studied the possibility of multistablity in the density and current of an interacting nanoscale junction as well as how to reversibly switch between the multiple solutions in time domain. An accurate theoretical treatment of electron correlation even in as simple model as an interacting electron gas at metallic densities still continues to be a challenge; especially description of features in the photoemission spectra due to electron correlations provides a theoretical challenge. The many-body perturbation theory yields a systematic way to study electron-electron (electron-phonon) correlations in various systems. One of the widely used approximations in MBPT is the GW approximation in which the bare interaction line is replaced with screened interaction line in the first order exchange diagram. The GW approximation gives good estimates for the band gap values close to experimental ones but especially the self-consistent GW approximation has a number of deficiencies like washing out of plasmon features and overestimation of bandwidths compared to experiment. One way to improve GW calculations is to include vertex corrections. Unfortunately, the straightforward inclusion of vertex corrections yields negative spectra in some frequency regions. We developed a diagrammatic approach to construct self-energy approximations with positive spectral properties. Our approach consists of expressing a self-energy of response diagram as a product of half-diagrams after which a minimal set of additional diagrams is identified to construct a perfect square. We applied this method to study vertex corrections in a homogeneous electron gas. In addition we analyzed the diagrammatic content of photocurrent with density functional theory. The expression for the photocurrent was obtained as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange correlation kernel of current density functional theory. The expression for the photocurrent gives us the angular dependence of the photocurrent but it does not provide a direct access to the kinetic energy distribution of the photoelectrons.

This thesis describes a study into the eigenvalues and eigenstates of twodimensional (2D) quantum systems. The research is summarized in four scientific publications by the author. The underlying motivation for this work is the grand question of quantum chaos: how does chaos, as known in classical mechanics, manifest in quantum mechanics? The search and analysis of these quantum fingerprints of chaos requires efficient numerical tools and methods, the development of which is given a special emphasis in this thesis. The first publication in this thesis concerns the eigenspectrum analysis of a nanoscale device. It is shown that a measured addition energy spectrum can be explained by a simple confinement of interacting electrons in a potential well. This result is derived using density-functional theory (DFT) and numerical optimization, guided by the asymmetric geometry of the device. The calculations also show that an observed decrease in the conductance can be explained by a change in the shape of the quantum wave function. The study of quantum chaos by statistical properties of eigenvalues requires a way to solve the eigenvalue spectrum of a quantum system up to highly excited states. The second publication describes a numerical program, itp2d, that uses modern advances in the imaginary time propagation (ITP) method to solve the eigenvalue spectrum of generic 2D systems up to thousands of eigenstates. The program provides means to sophisticated eigenvalue analysis involving long-range correlations, and a unique view to highly excited eigenstates of complicated 2D systems, such as those involving magnetic fields and strong disorder. After the spectrum is solved, the next step in the eigenvalue analysis is to remove the trivial part of the spectrum in a process known as unfolding. Unless the system belongs to a special class for which the trivial part is known, unfolding is an ambiguous process that can cause substantial artifacts to the eigenvalue statistics. Recently it has been proposed that these artifacts can be mitigated by employing the empirical mode decomposition (EMD) algorithm in the unfolding. The third publication describes an efficient implementation of this algorithm, which is also highly useful in other kinds of data analysis. Quantum scarring refers to the condensation of quantum eigenstate probability density around unstable classical periodic orbits in chaotic systems. It represents a useful and visually striking quantum suppression of chaos. The final publication describes the discovery of a new kind of quantum scarring in symmetric 2D systems perturbed by local disorder. These unusually strong quantum scars are not explained by ordinary scar theory. Instead, they are caused by classical resonances and resulting quantum near-degeneracy in the unperturbed system. Wave-packet analysis shows that the scars greatly influence the transport properties of these systems, even to the extent that wave packets launched along the scar path travel with higher fidelity than in the corresponding unperturbed system. This discovery raises interesting possibilities of selectively enhancing the conductance of quantum systems by adding local perturbations.

The understanding and control of the dynamics of hybrid modes consisting of strongly coupled surface plasmon polaritons and molecular excitations of dye molecules is of great timely interest, as it allows one to tailor interactions between optical signals as needed for active all-optical devices. Here we utilize dye molecules with an especially large Stokes shift to demonstrate the absence of mutual scatterings among the strongly coupled hybrid modes. We employ a quantum mechanical three-level model and show that the hybrid modes decay via dephasing and internal relaxation of the molecules to a fluorescing state of the dye, which can be used as a measure for the decay. Our results provide essential information about the dynamics of the strongly coupled modes. peerReviewed

Esittelemme yksiulotteisen, ajasta riippumattoman, Schrödingerin yhtälön ja siihen liittyviä potentiaalikuoppia, eli reunaehtoja. Lisäksi esittelemme kolmeulotteisen, radiaalisen, Schrödingerin yhtälön ja tutkimme siihen liit- tyvän keskeissymmetrisen, vedynkaltaisen atomin potentiaalikuopan ener- gian ominaisarvoja. Käymme läpi tärkeimpiä yksiulotteisen differentiaa- liyhtälön ääriarvo-ongelman ratkaisemiseen soveltuvia numeerisia integroi- jia, joista johdamme yksinkertaisimmat ja lisäksi tutustumme muutamiin matriisimenetelmiin. Analysoimme eri menetelmien tarkkuutta ja yleistä soveltuvuutta Schrödingerin yhtälön energian ominaisarvojen etsimiseen silmämääräisesti ominaisfunktioyritteen graafista sekä automaattisesti. Havaintomme eri menetelmien tarkkuuksista ja löydetyt ener- gian ominaisarvot ovat linjassa kirjallisuudessa ja julkaisuissa esitettyjen arvojen kanssa.

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may ‘‘directly’’ influence them, but (iii) other inputs provide a ‘‘context’’ for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or not empirically realizable: those that form special cases of the classical type, those that fall between the classical and quantum ones, and those that violate the quantum type. We show how one can quantify and classify all logically possible contextual influences by studying various sets of probabilistic couplings, i.e., sets of joint distributions imposed on random outputs recorded at different (mutually incompatible) values of inputs. peerReviewed

Termodynamiikan yksinkertaisia ja yleispäteviä perusperiaatteita voidaan soveltaa luonnontutkimuksessa monilla eri alueilla. Albert Einstein totesi vuonna 1949, että termodynamiikka on kattavista fysikaalisista teorioista ainoa, jota ei varmasti tulla koskaan hylkäämään. Termodynamiikan toinen pääsääntö hallitsee kaikkia palautumattomia,irreversiibeleitä, prosesseja. Tieto siitä, että lämpö ja energia ylipäätään siirtyvät aina korkeammista arvoista kohti matalampia, koskee myös mikroskooppisten hiukkassysteemien kehitystä. Tilastolliseen mekaniikkaan perustuva termodynamiikka ei kuitenkaan perinteisessä muodossaan sisällä riittäviä välineitä mikroskooppisten järjestelmien kuvaamiseen. Se pitäytyy todellisuuskuvailussaan suljettuihin hiukkassysteemeihin, kun taas hiljattain muotoiltu avointen järjestelmien tilastollinen mekaniikka tarkastelee todellisuutta energiamaisemana, jonka tiheyserot pyrkivät virtausten myötä tasoittumaan. Tämä energian ja vaikutuksen käsitteisiin perustuva kokonaisvaltainen kuvaus tarjoaa tarkastelunarvoisen kehikon, jossa entropian kasvu voidaan sovittaa yhteen evoluution ja yhä mutkikkaampien rakenteiden syntymisen kanssa. Myös monet kvanttimekaniikan keskeiset tulkintaongelmat aina mittausongelmaa myöten saavat uutta valaistusta.

Halkaisijaltaan muunnellun kvanttiaaltojohtimen kapenemat toimivat tehokkaina potentiaalivalleina elektronin pitkittäissuuntaiselle liikkeelle. Kaksi kapenemaa muodostaa kvanttiresonaattorin, jossa resonoiva tunnelointi voi tapahtua. Tämä tarkoittaa sitä, että elektronit, joiden energia on lähellä resonanssia, läpäisevät resonaattorin todennäköisyydellä lähellä yhtä.Sarafanov kuvailee väitöskirjassaan asymptoottisesti elektroniaallon etenemistä kvanttiaaltojohtimessa, jossa on kaksi kapenemaa. Aaltoluvun k oletetaan olevan ensimmäisen ja toisen kynnysluvun välissä, jolloin vain sisään tuleva ja poismenevä aalto voivat edetä jokaisessa aaltojohtimen päässä äärettömyydessä. Väitöskirjassa esitetään asymptoottiset kehitelmät aaltofunktioille, ja heijastus- ja siirtymäkertoimille, kun kapenemien halkaisijat menevät nollaan. Lisäksi Sarafanov esittää asymptoottiset kaavat resonaatiotaajuuksille ja analysoi kertoimien käyttäytymistä lähellä resonanssipistettä. Monet elektroniset laitteet, kuten transistorit ja vahvistimet voivat perustua halkaisijaltaan muunneltuihin aaltojohtimiin. Sarafanovin esittämiä kaavoja voidaan hyödyntää näiden laitteiden ja niiden optimaalisen toiminnan suunnittelussa. The narrows of a quantum waveguide with variable cross-section play the role of effective potential barriers for the electron longitudinal motion. Two narrows form a quantum resonator where a resonant tunneling can occur. It means that electrons with energy close to a resonant value pass through the resonator with probability near to 1.We give an asymptotic description of electron wave propagation in a quantum waveguide with two narrows. The wave number $k$ is assumed to be between the first and the second thresholds, so only one incoming and one outgoing wave may propagate in every outlet of the waveguide to infinity. We present the asymptotic expansions of wave functions, the reflection and transition coefficients as the diameters of narrows tend to zero. Moreover, the asymptotic formulas for the resonant frequencies are obtained and the behavior of the coefficients is analyzed near a resonance.

Kvanttimekaniikan varhaisvaiheesta alkaen nousi esille kysymys, vaikuttaako havaitseminen havainnon kohteeseen, ja jos vaikuttaa, niin millä tavalla. Kysymys herättää edelleenkin kiinnostusta, kuten esimerkiksi vast'ikään Tieteessä tapahtuu -lehdessä julkaistu artikkeli Kallio-Tamminen 2000 osoittaa. Seuraavassa esitän asiasta vain eräitä aivan elementaarisia ajatuksia, jotka fysiikan tutkijalle ovat itsestään selviä. Sen enempää matemaattisiin kuin "filosofisiinkaan" aspekteihin en puutu. Tarkastelen asiaa "tavallisen lukijan" kannalta, jolle jotkut asiasta esitetyt näkemykset kenties tuntuvat hieman häkellyttäviltä. Syynä tähän saattaa olla mm. se, että sanaa "havainto" käytetään tässä yhteydessä monessa mielessä, jotka eivät aina tunnu vastaavan sitä, mitä tavallinen lukija tuolla sanalla tarkoittaa.

Kvanttimekaniikan ns. Kööpenhaminan tulkinta edellyttää syvällisiä uudistuksia todellisuuskäsitykseen, kun taas kvanttimekaniikan myöhemmät tulkinnat ovat pyrkineet pitäytymään klassisen fysiikan perusoletuksiin kuten determinismiin, reduktionismiin ja syrjässä olevaan havaitsijaan. Tulkintojen välinen konflikti kulminoituu kvanttimekaniikan mittausongelmassa. Koko sitkeä ongelma häviää, jos ihminen nähdään Niels Bohrin tavoin evolutiivisena agenttina, joka voi osaltaan suunnata maailman irreversiibeleitä, palautumattomia prosesseja.

Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon., Roadmap article with contributed sections and subsections on: 1. Metrology and sensing 2. Quantum light sources, cavities and detectors 3. Quantum computing with spins 4. Nano and opto-mechanics 5. Low-dimensional systems 6. Molecular devices 7. Nanoplasmonics (47 pages, 25 figures). Contains arXiv:1907.02625, arXiv:1907.07087, arXiv:2001.11119, arXiv:2011.13907